Good news is I think saves were always compatible in Milfy City except one time were the inventory was broken and that got fixed as well.
At least in my experience it's quite rare that saves are made incompatible by choice although it did happen recently with Timestamps. But it definitely is something that needs testing and it gets more complicated because not everyone will continue on from a save at the end of the last version (e.g. somebody might not have explored a certain path yet and that one might get screwed up if you purchase a certain item that got introduced in the latest update too soon/too late).
Basically the less linear a game gets the more complex testing might need to become - both to avoid continuity errors (one branch referencing stuff that happens in another branch when the player might not have explored that branch yet) and technical issues (were the game expects certain variables to be set when they are not).
And then (especially with Ren'py Games in my experience) there is the issue of people hacking the save files to e.g. increase money or set certain variables to skip something and that might lead to instances of variable combinations that can't occur in regular gameplay and therefore causing issues that don't come up in testing (I believe the latest release of Midnight City had a patch to take care of such an issue).
Overall - testing can be a bitch and it's not really something where it's easy to predict how much effort will be required.