Hey, thanks for playing! You played this really soon and we haven't filled out the page completely yet, will add some instructions to it at some point :)
The way I displace is that I have a bunch of points which gradually move vertically to the mouse when it's held. I have a polygon collider for the terrain, but for optimization reasons, only part of the points get set on the polygon (this happens dynamically throughout the game).
I don't know if I'm clear, but either way you can just see how I did it - https://github.com/icy-lava/frost-surf/blob/main/object/terrain.gd
Thanks for playing!