> "Imagine a text editor where all your text documents are gone after you cleared the browser data"
One way to address that issue is the native file system access APIs[0] coming soon, available today in Chrome Canary and Edge Canary. There, you'd be able to save your documents to the user's file system, just like a native app would. Those files will be exempt from any browser data clearing.
> all infos about which exercises you did and when is gone for good of course.
Might be good to store that data on the server. I realize not all PWAs have a proper backend server, but that sounds like a good candidate.
[0]: https://bugs.chromium.org/p/chromium/issues/detail?id=853326