Hello, sure!
Just for clarification, it's mainly for mobile. I haven't encountered save problems for computer. :)
For now Opera GX seems to completely not work. Google/Chrome mostly seems fine, but saving does sometimes bug (I'm not sure what the condition for it is) and Kiwi Browser and Brave work the best.
It's not necessarily game's problem as it may be more of a browser problem (some other games are similar in terms of saving with this browsers).