Is there « a biological predisposition to organize ourselves around something “greater than” us » AND « Can « something “greater than” us be an animal » ?
The first « greater than us » element that any living being has to learn to live with are the rules/ ways by which the world/environment around is working with. Early humans certainly did the same.
Within these basic facts/rules, there are the things which are beneficial for these animals/early humans (water, plants which feed/ cure, animals good to eat or harmful, etc etc). At this point, some stories (myths) & rituals certainly are useful to pass on the knowledge. The myths explain why things occur/are as they are and why it will continue in future. The rituals unite the group members on the common beliefs. The myths explains who can/cannot marry who, define which actions are good/bad, etc
It may occur that an animal (or a plant) is believed to have saved the life (or protected) the first woman (or the first man). This animal/plant can become a totem for the Group.
When the Group gets bigger, with more complex social rules (with or without royalty), several sub-groups having different « totem » can be seen within the same ethnicity/ tribe.
So, yes, I agree that a plant or an animal can be considered as something « greater than us ». But in many instance, the greatest « greater than us » is a god (which, in Africa, generally is believed to have retired somewhere, in a remote place, after having created the world.) I also understant that the greatest « greater than us » in traditional Asia is the Cosmos (i.e. the physico-chimical & general rules which run the universe, Gods -if any- included).
On the biological predisposition to organize ourselves around something « greater than us », I would say No. Evolution started with tiny physico-chimical elements. Most of them disappeared. Some happened to be compatible with the environment around them, and some survived (=adaptation process). There never were any « predisposition » for plants/animals including humans. This idea gained grounds with the « latest » monotheisms. But I see that as an « hypothesis/ belief/ way to explain the world » which belongs to these specific families of beliefs.