You are not alone, fellow penguin-wrangler.
Though I am, in fact, quite an amateur wrangler of penguins.
I haven't had the game for long enough to comment much on the speed or lack thereof when it comes to Linux support. I will note, though, that I'm a little confused by one part of your post. When I get on GoG, I do indeed have access to 2.2.3 (just double-checked). If you
don't, it may be an issue with your GoG account rather than Paradox?
One odd and slightly annoying bug with 2.2.3 for Linux has been that I can no longer run the game directly with start menu shortcuts for some reason. I have to go into the Stellaris directory and run ./start.sh in terminal directly - and the terminal has to remain open while it's running or the game crashes. Not sure why; it worked fine in early versions of Le Guin. In fact, to be fair, I don't even know for sure whether it's an issue with 2.2.3 or some strange side effect of some recent kernel upgrades.
Anyway, don't know if any of this helped you, though I hope it at least gave you a mild sense of companionship to know that there are other GoG-Linux-Stellaris people out there. Either way, stay strong, and remember not to let any light apertures or fruit objects contaminate your synthetic ascension process
