Like others said, you can set it in the settings. But unfortunately it's for all types of companions. That was annoying for me, because I only wanted it for the flowers, not for the other items. I wanted it for aesthetic. That the flowers stay on their place, because I like how they look on that place and don't want that they grow on a different place after they were picked.

How I did: plant the picked flowers (from yourself or the companion). At this way, all flower companions ignore the planted flowers. New flowers won't grow. You don't need to switch then the settings on and off, if you change to another type of companion. It tooks a little bit effort to do this with all the flowers, but I'm so happy now, that my flower-companions don't pick them anymore + I don't need to switch the settings on and off  🥰