Do with extra food once a planet is fully populated

You occupy the planet, you do not control it, this works similar to EU4.

The occupation grants a large amount of warscore and you can send your armies away, Your opponent has to reinvade to liberate the planet.

Whether you get the planet in the end depends on the war goals, the occupation merely provides additional warscore, with which you can press your demands.

Most importantly though, it prevents the enemy from using the planet and getting resources from it without you having to constantly bombard it and requiring an invasion from your opponent to liberate it.

Stone Age primitives are actually a third state in-between the pre-sentient races that you can uplift and the fully sentient primitive civilizations that you can observe.

This is explained on the Stellaris Wiki's Pre-FTL Species Page:

There is a third possibility of non-FTL races, which are the stone age primitives. They appear as modifier on planets. If the policy for native interference is not Unrestricted, then the empire will be unable to colonise the planets. Therefore a pacifist or xenophile empire (or the fanatic versions) can't chose "unrestricted", and will be unable to colonise these planets.

So you might not be able to interact at all. Perhaps they will advance to the Bronze Age at some point and you can observe them. It's not clear if that's a possibility.

If you can colonize, though, here's what you can do once you get there:

Known Variations:

• Voluntarily retreat to Enclaves rather than contest the primitives for the land: Places a number of primitives on the surface map as tile blockers. Apparently these blockers cannot be removed, though they provide Social Science adjacency bonuses.
• Antagonize the aliens: fewer tile blockers
• Enslavement: No tile blockers. The new species appears as enslaved pops on the planet. The slaves can be emancipated, and integrated into the empire. Useful if a pop is neeeded to colonize worlds of the same type as their homeworld. Option is only available if slavery is enabled as a policy.

I think I actually had this happen on a planet in my current game, but I was confused because there was also a Pre-Sentient race on the planet. I uplifted that race, and was surprised to find that the Stone Age primitives continued to live in the reservations.