Unfortunately there just doesn't seem to be a lot of love for Linux when it comes to some of these texturing packages.
The only real two I've been able to scope out are Substance Painter on Steam, which can be somewhat expensive.
Another option is ArmorPaint, which is a simpler texture painting app that could potentially work. I think tutorials on this software are fairly sparse, but from what I've seen there have been some cool textures created using it!
Substance Painter System Requirements
Have you tried running it thru wine. You will of course need to configure your wine setup to use 64 bit since wine defaults to 32 but.(Unless newer version default to 64). I use play on Linux which uses wine but it also uses more resources. The 64 bit wine in Play on Linux is quite buggy. My understanding is using wine directly has fewer issues. You could also try using proton which is what steam uses to run Windows programs on Linux. I haven't used it outside of steam so don't know much about it.
Amazing quick replies and suggestions here! I'm a bit blown away.
Just to follow up, I asked the InstaMAT account on Twitter and got the following reply:
"There are indeed good news: the vfx-platform CY2024 now includes support for some of the components that we need, this means we can port to vfx linux without backporting to older versions! This is likely going to accelerate the process, however, no ETA yet."
