you should implement that feature into your future versions of the game cause me personally my saved files don't always work and it's sometimes a hastle to restart all to just get round 30+ minutes of new content.
I don't know anything about the web versions, you would have to ask whoever made them. If you start a new game on the itch version, your save will work on the next update.
Changing versions almost always breaks saves. You can't play web then offline, or modded then not modded. That's just how Renpy works