I leave the session automatically saved and reopen the last one when starting Kate however, it opens empty, I lose all the information from the saved files as well as search settings.
Confirmed in 25.04.1. This looks to be a heisenbug, affecting maybe 10% of session starts. Possibly an error in session saving. Kate seems to encounter an error during session loading and use a blank session, overwriting the current session file.
Please try the latest Kate. This is fixed now I believe. https://cdn.kde.org/ci-builds/utilities/kate/master/windows/
If its not fixed, feel free to reopen the bug.