Thank you for the report, the data issue fixed with the version released just now!
Regarding the battles we are working on a fix :)
This has been changed now, see https://kringel-games.itch.io/progress-station/devlog/725012/update-101
This seems to work in the latest Firefox (123.0.1) on Windows.
Could you maybe sent us your https://www.whatsmybrowser.org/?