Ey!! I made some tests by playing my own game that had a saving system, and I discovered that the problem with that all along was my browser.
You see, I've been mainly using Brave lately because it's the browser my brother invented from I don't know where and setted as the default on my laptop, but since it's not part of the main trinity (Chrome, Edge and Firefox) I assume it might have some sort of conflict with however Construct saves stuff for html.
So yeah, you shouldn't worry much about that, fixing this might be way more trouble than it is worth. I tested on chrome and there it works just fine.