It'd be nice to have additional ways to sync other than gPodder and Nextcloud, maybe saving some sort of log or file that also tracks the status of played episodes and whatnot.
That's what the database is for (~/.local/share/KDE/kasts/database3.db). You can copy or sync that file to other locations/installs of Kasts. There's no need to duplicate that info in yet another file. Of course, you need to manually keep track of sync conflicts if you do it this way. There are currently no other established ways to sync with other applications. There are a few that are being developed (e.g. openpodcastapi), and Kasts will try to support those if/when they become available.