I really like the idea of controling the plant as it also seems to have a mind of its own!
The game and control speed is definetly affected by the refresh rate (I tried the game on 200Hz and 60Hz and the difference is noticable) I don't quite know how this is handled in Godot but the equivalent in unity would be scaling the growth and input controls by Time.deltaTime.
Other than that I really enjoyed the game, especially the looks of the plant growing were really interesting!