I hesitated posting this video because of the low framerate. Hope nobody will believe this has to do with Godot.
The main problem here, by far, is that the tree mesh I've found models each leave with multiple triangles (which is fine for some use cases, but not adapted for this). There are 170000 triangles per tree.
Once I manage to reduce the triangle count it should run at 60fps. And hopefully I will also be able to increase the tree density (and add variations and bushes etc.)

