Hello, I got help on discord on how to get around this issue. Apparently, one of the PR broke the save feature ( https://github.com/FAForever/fa/pull/6647/files ).
To fix this, you need to find "/gamedata/lua.nx2". Create backup for safety and rename the file to "lua.zip", find and extract file "userInit.lua". Inside, find this line (should be near the top) "doscript '/lua/ui/globals/InternalSaveGame.lua'". Delete it or comment out, save the file and put back into lua.zip. Then rename it back to "lua.nx2". After doing this, saving and loading started to work again for me.
I have uploaded lua.zip file after the changes I made, you can use that. Just rename it to "lua.nx2" and paste into "/gamedata", just be sure to make backup.