If you want to collect berries passively you can get a tamed daeodon, then place it in front of a cluster of 2 or 3 berry bushes that are really close to each other (preferably in your base so you have easy access).

The daeodon will automatically collect berries from the bush, then after the bush respawns, it will collect berries from the bush again. It will keep repeating this process until it starts to get encumbered, then stop. After that, you can collect the berries and berry seeds from its inventory.

Or, you can just farm them with crop plots.

Brontos, theris, megatheriums, and stegos will not collect berries automatically (that also means when they wander), but daeodons can.