[2022] Can't pick our empire when we try loading a multiplayer save file

I don't think I'll be able to help with this, but I believe there have been other such reports occasionally. So far as I recall the only way to rescue that save it to manually edit the save game file to make the empire visible again.

You might check the MP and Bug Report forums for other such reports.

Sorry to not be able to help you much on this occasion!  

I'm not across bug reports for this game, but my impression it is is a very sporadic issue and the devs have not been able to reproduce it. So the short answer is that (so far as I know) we don't know why it happens!

If you are using any mods, try without I guess.