While it would be great to have true cross-device/platform syncing, I am sensitive to the potential complexity of such functionality.

Assuming that Xavier isn't close to bringing us a proper bi-directional cross-platform solution, I would like to suggest an alternative which may be acceptable to many of the people who have asked for cross-device syncing at https://podcastaddict.uservoice.com/forums/211997/suggestions/4115735 and a desktop version at https://podcastaddict.uservoice.com/forums/211997/suggestions/6531942.

Namely:
That a primary-secondary model be created.
One Android device would be configured as the primary device. All other Android devices and desktop or web applications would be secondary.
The primary device would be responsible for management of subscriptions, including retrieving new episodes.
The secondaries would only be able to play episodes from the catalogue (podcasts or playlists), and log status updates to those episodes. Perhaps they could be used to request the primary device to add a new subscription. Android devices would run the same app but it would be in a mode which blocks the functions which aren't appropriate for a secondary.

The primary device would periodically write out the relevant data (like a backup) to an appropriate location (perhaps a cloud storage account) and in addition to those main repositories it and also the secondaries would record status changes ("incremental backups" if you like) in a separate pool of data. The primary's updates would include new episodes. All devices would read from all files to determine the current status. The primary would also track the changes from the secondaries and update itself, and every so often clear all the data and create a new set. The podcast update process is a good opportunity to do this as in any case the primary device needs to be on-line for that to happen.

Maybe this "sync" method could be straightforward enough that the secondaries (especially non-Android) could even be third-party programs, exchanging data with the primary via file formats which Xavier determines?

I'm looking forward to seeing if Xavier and the user base are interested in this.