We cannot know these things with certainty, but it seems nonhuman primates don't understand themselves to be playing roles with intentional coordination or division of labor

The role of roles in uniquely human cognition and sociality. Michael Tomasello. Journal of the Theory of Social Behavior, August 16 2019. https://doi.org/10.1111/jtsb.12223

Abstract: To understand themselves as playing a social role, individuals must understand themselves to be contributing to a cooperative endeavor. Psychologically, the form of cooperation required is a specific type that only humans may possess, namely, one in which individuals form a joint or collective agency to pursue a common end. This begins ontogenetically not with the societal level but rather with more local collaboration between individuals. Participating in collaborative endeavors of this type leads young children, cognitively, to think in terms of different perspectives on a joint focus of attention ‐ including ultimately an objective perspective ‐ and to organize their experience in terms of a relational‐thematic‐narrative dimension. Socially, such participation leads young children to an understanding of self‐other equivalence with mutual respect among collaborative partners and, ultimately, to a normative (i.e. moral) stance toward “we” in the community within which one is forming a moral role or identity. The dual‐level structure of shared endeavors/realities with individual roles/perspectives is responsible for many aspects of the human species' most distinctive psychology.

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2.1 Social roles in great apes and early humans?

Humans' nearest primate relatives, chimpanzees and bonobos, live in complex social groups. From an external (functionalist) perspective it is of course possible to speak of the various roles individuals are playing in the group. But does this notion have any meaning for them? Does it make sense, from their point of view, to say that the dominant male chimpanzee is playing the role of peacemaker in the group?
While we cannot know these things with certainty, the proposal here is that neither chimpanzees nor bonobos (nor any other nonhuman primates) understand themselves to be playing roles in anything. Although many, perhaps most, of their social interactions are competitive (even if bonobos are less aggressive), they also cooperate in some ways, and so the notion of role is at least potentially applicable. As a frequently occurring example, if one chimpanzee begins fighting with another, it often happens that the friends of each of the combatants join into the fray on the side of their friend. It is unlikely that they see themselves as playing roles in this coalition. More likely, each individual is participating for her own individual goal, sometimes helping the other in that context. But they are basically just fighting side by side, without intentional coordination or division of labor toward a common goal. As another example, when chimpanzee or bonobo pairs are engaged in mutual grooming, we could say from the outside that one is in the groomer role and one is the groomee role. But again this interpretation may be totally our own; they may just be searching for fleas and enjoying being cleaned, respectively. And, for whatever it is worth, both agonistic coalitions and grooming are social interactions that are performed by all kinds of other species of mammals and even birds.
By far the most plausible candidate for an understanding of social roles in nonhuman primates is chimpanzee group hunting. What happens prototypically is that a small party of male chimpanzees spies a red colobus monkey somewhat separated from its group, which they then proceed to surround and capture. Normally, one individual begins the chase and others scramble to the monkey's possible escape routes. Boesch (2005) has claimed that there are roles involved here: the chaser, the blocker, and the ambusher, for instance. Other fieldworkers have not described the hunts in such terms, noting that during the process (which can last anywhere from a few minutes to half an hour) individuals seem to switch from chasing to blocking and to ambushing from minute to minute (Mitani, personal communication). In the end, one individual actually captures the monkey, and he obtains the most and best meat. But because he cannot dominate the carcass on his own, all participants (and many bystanders) usually get some meat (depending on their dominance and the vigor with which they harass the captor; Gilby, 2006). Tomasello, Carpenter, Call, Behne, and Moll (2005) thus propose a “lean” reading of this activity, based on the hypothesis that the participants do not have a joint goal of capturing the monkey together – and thus there are no individual roles toward that end. Instead, each individual is attempting to capture the monkey on its own (since captors get the most meat), and they take into account the behavior, and perhaps intentions, of the other chimpanzees as these affect their chances of capture. In general, it is not clear that the process is fundamentally different from the group hunting of other social mammals, such as lions and wolves and hyenas, either socially or cognitively. Experimental support for this interpretation will be presented below.
The evolutionary hypothesis is that at some point in human evolution, early humans began collaborating with one another in some new ways involving shared goals and individual roles. The cognitive and motivational structuring of such collaborative activities is best described by philosophers of action such as Bratman (2014), Searle (2010), and Gilbert (2014), in terms of human skills and motivations of shared intentionality. The basic idea is that humans are able to form with others a shared agent ‘we’, which then can have various kinds of we‐intentions. In Bratman's formulation, for example, two individuals engage in what he calls a shared cooperative activity when they each have the goal that they do something together and they both know together in common conceptual ground that they have this shared goal. This generates roles, that is, what “we” expect each of “you” and “me” to do in order for us to reach our shared goal. Gilbert (2014) highlights the normative dimension of such roles. When two participants make a joint commitment to cooperate, for example, each pledges to the other that she will play her role faithfully until they have reached their shared goal. If either of them shirks her role they will together, as a shared agent, chastise her – a kind of collaborative self‐regulation of the shared agency. This special form of cooperative organization scales up to much larger social structures and institutions such as governments or universities, in which there are cooperative goals and well‐defined roles that individuals must play to maintain the institution's cooperative functioning.
Tomasello (2014, 2016) provides a speculative evolutionary account of how humans came to engage with one another in acts of shared intentionality. There were two steps. The first step came with early humans (i.e., beginning with the genus Homo some 2 million years ago to approximately.4 million years ago). Due to a change in their feeding ecology ‐ perhaps due to more intense competition from other species for their normal foods ‐ early humans were forced to collaborate with one another to obtain new kinds of resources not available to their competitors (e.g., large game and also plant resources requiring multiple individuals for harvesting). In these early collaborative activities, early human individuals understood their interdependence ‐ that each needed the other ‐ and this led them to structure their collaborative activities via skills and motivations of joint intentionality: the formation of a joint agency to pursue joint goals via individual roles. As partners were collaborating toward a joint goal, they were jointly attending to things relevant to their joint goal – with each retaining her own individual perspective (and monitoring the other's perspective) at the same time. Such joint attention means not only that individuals are attending to the same situation, but each knows that each is also attending to their partner's attention to the relevant situation, etc.: there is recursive perspective‐taking. When individuals experienced things in joint attention those experiences entered their common ground as joint experience or knowledge, so that in the future they both knew that they both knew certain things.
The second step came with modern humans (i.e., beginning with Homo sapiens sapiens some 200,000 years ago). Due to increasing group sizes and competition with other groups, humans began organizing themselves into distinctive cultures. In this context, a cultural group may be thought of as one big collaborative activity aimed at group survival, as all individuals in the group were dependent on one another for many necessities, including group defense. To coordinate with others, including in‐group strangers, it was necessary to conform to the cultural practices established for just such coordination. Knowledge of these cultural practices was not just in the personal common ground of two individuals who had interacted in the appropriate circumstances previously, as with early humans, but rather such knowledge was in the cultural common ground of the group: each individual knew that all other members of the group knew these things and knew that they knew them as well even if they had never before met. Making such cultural practices formal and explicit in the public space turned them into full‐blown cultural institutions, with well‐defined roles (from professional roles to the most basic role of simply being a group member in good standing) that must be played for their maintenance. The new cognitive skills and motivations underlying the shift to truly cultural lifeways were thus not between individuals but between the individual and the group – involving a kind of collective agency ‐ and so may be referred to as collective intentionality.
The proposal is thus that the notion of social role, as understood by participants in a social or cultural interaction, came into existence in human evolution with the emergence of shared intentionality, as the psychological infrastructure for engaging in especially rich forms of collaborative, even cultural, activities. The notion of social role is thus indissociable, psychologically speaking, from cooperation. The evolutionary precursor to the notion of a societal role, as typically conceived by sociologists and social psychologists, is thus the notion of an individual role in a small‐scale collaborative activity; societal roles in larger‐scale cultural institutions build on this psychological foundation.