Just in case anyone wants to check the Wine compatibility, rather than taking a chance as I did, this installer is working nicely without any special setting-up.

I'm using (2 PCs the same) Ubuntu Studio 20.04, PlayOnLinux 4.3.4 with the installer provided through the service. Wine 3.03 emulating Win98. The only additional 'Install Component' I needed was Directplay. Nvidia proprietary driver - legacy driver 390. Plus also playing on the same network a newer Win7 PC that had to be told to run it in Win98 compatibility mode.

This version practically worked out of the box (apart from PlayOnLinux not automatically installing Directplay for multiplayer). It looked as if PlayOnLinux was just overriding 4-5 libraries so hopefully it would be easy on plain Wine or Lutris as well.

GOG I've usually found to be good with repackaging stuff to work on modern PCs, but on Total Annihilation it makes the difference of running it at all because it always was so awkward getting this game to run multiplayer, when it's one of the greatest multiplayer games of all time.

Just want to add that I got TA to work online on GameRanger on Ubuntu 20.04 as well.

the process was:
- Install Wine: needlessly difficult for something as essential. I did it through the "app store", was buggy and messy but it worked.
At this point, TA is playable offline through wine with no further tinkering. Any alt-tabbing will cause the game to crash either before the map loads, or at the end screen if you're already in a map. This is an issue with GameRanger, since you loose focus from TA just before you enter the game due to some GR notification windows. so next step: rune Wine in windowed mode.
- Winecfg: go to graphics tab, check "Emulate a virtual desktop". Done.
Next, you'll need DirectPlay to play TA online:
- Install Winetricks. Run it. Install DirectPlay. Any missing .dlls can also be installed through Winetricks.
- Install GameRanger through Wine.
- Install any mod. TA Escalation is the most popular mod, but I would also keep a seperate copy of TA 3.1, there are a few people that prefer the original experience. I've yet to try ProTA but it's on my list, and looks like it's got quite a few players supporting it.

Run GameRanger through Wine. That's it, TA and mods fully playable online through GameRanger.