That sounds like the game creates new units based on the BP of the units in full share. Would be the same base issue as upgrades done post creating of the units not feeding into the veterancy bonuses I saw somewhere else.
There is some mod that transfers all your units to one player automatically when you die, that idea probably could be merged into the full share function to allow for a better full share feature solving this issue.
Maybe the Game Team can investigate the viability of my proposal and implement it if feasible.

@jip I did not see an option for UI scaling, but I changed the resolution to 1920x1080.

It is an old game - I'd recommend to switch before hand. There have been numerous issues regarding sounds (stereo vs 5.1, etc) and there're all of the type 'unfixable' as they are related to the engine.

I'm having issues playing Aeon mission Shining Star in co-op. When launching the map in a team with Common Army enabled, the map loads but never starts any script so all we see is a mostly unexplored map, with no voice over or mission objectives appearing, no ACU warps and no units to control. Seems to be frozen. In our testing it seems to work when we disable Common Army, I can reproduce this even with a bot team-mate instead of a human. Logfile from that game here.

We've been playing the previous Aeon missions without any problem, and the first 2 of the UEF ones - no issues with those when Common Army is enabled.

It sounds like similar behavior to this:

This is something done by the engine. I suspect it has to do with not retargeting something it can't reach. Not sure how / when it resets and if we can reset it ourselves.

That is some weird behaviour indeed. To me it looks like the arty wants to keep a moving target in the inner circle, which is it's minimum range.