Having a cat in the icon kinda goes against Gnome’s Human interface guidelines, though just the scratch marks work work pretty well imo, especially with the number of apps that have paper as their icon.
Scratch Mark seems like a pretty good name, considering that it feels like more of a writing name compared to Copycat, which feels like more the name of something like flatbed scanner software.
I basically do exactly this, but I am running the reverse proxy on my home computer: the VPS is literally just acting as a proxy, for which I use wireguard to tunnel the connection. So far it’s worked great, though initial setup was a pain.