From what I've read, it may be related to having cross-saves enabled and that the amount of requests going through to the destination server overloads it. Which correlates with a typical 502 bad gateway error. Turning off cross-saves may help, but not sure.
Yeah it could do with being a bit clearer, could also do with managing multiple saves in a better way - and probably grouping them by character.
Other platforms has this. It's called 'Player Profiles' which I've always argued is a bit misleading terminology for what I believe an average gamer interprets it as. In times more than I can count on my hands, people have been mindblown when I've advised making a new player profile for each campaign they start; So one profile for their solo campaign, another profile for playing a separate coop campaign with a friend. Player profiles separates savefiles from eachother, convenient for different characters/campaigns. It also saves mod list and load order for when modding is supported. TL;DR - When starting a new game, make a new profile is how I recommend playing Larian games.
However, Stadia doesn't have player profiles. I don't know the reason, but I've expressed my opinions and requests on it a few times. I can only assume it's some limitation on Stadia's side in regards to file management from a user.