I have trouble with saving in the browser and on the Windows version played on Porting Kit on MacOS.
I can start a game and play for awhile, but if I exit in any way, it always starts over launching the beginning of the tutorial. In other words, I lose all progress I make -- no progress saves once I exit the game.
I first played normally in the browser and discovered the problem, then tried again in the browser after turning off all privacy etc protections in case that was the problem (not needed on other Itch.io games, but I thought it was worth trying); same problem. Finally, I went through the hassle of installing the Windows version and getting it to run on MacOS via porting kit.
In all cases, the game essentially resets to zero whenever I exit and restart the game. Very frustrating, especially after my first play of a couple of hours...
Having said that -- the game itself is super fun! I hope you iron out the bugs and get it working (natively on MacOS eventually?? or a paid full browser version that saves?)