Hi there, just chiming in.
Berry bushes are more like a weed than a tree, you have to actively combat some of them to keep them in check, at the very least they are not particularly picky about where they grow or their needs.
The new system for berry bushes needs to be stripped back (Har) and replaced. Have them shatter on trying to pick them up, keep the cutting option but put it on a tool, the humble secateurs (basically gardening scissors) with a toggle option to either cut or prune.
Why prune? Because berry bushes need pruning to get the most out of them, this would be how you enable the player interaction > reward loop.
Tl;Dr Don't treat bushes like crop plants, treat them like bushes.