If you're getting specific errors, don't hesitate to create an issue in the respective project. We're (slowly) working towards a new (better) sync solution, but the existing implementation should still work.

Does antannaPod put logs somewhere? Right now I'm not able to provide more than "does not work for me"

If something fails, an error message should be shown (either in Nextcloud or AntennaPod). You can export the full logs via Settings » Report bug » three dots in the top-right. If you create an issue (bug report), please describe what doesn't work exactly (the process may go wrong at many different steps, from entering your password to a specific episode state being synced on AntennaPod but not showing up in the gPodder sync app).