There's this open feature request for the passout protection feature:
https://features.jellyfin.org/posts/814/are-you-still-watching-prompt
So I guess that probably means things will play continuously?
Personally I've never noticed it stopping, it just autoplays the next episode until they run out, but perhaps I've never watched for long enough in one session.
I think on an ideological level you should give jellyfin a try regardless of this feature because it's completely open source and community driven, no features are pay walled.
I've been using SSHelper together with rsync for years and it works perfectly. You can log in the first time with a password, and place your public key to use key based auth going forward.
In addition to doing this over WiFi I also often use a usb to ethernet adapter (usb side plugged into phone) to get better performance if I'm doing larger transfers, for example copying off a large number of photos.
Edit: looks like there's a note on the play store page about incompatibility with newer Android versions. Disappointing. I guess I'll have to find another solution when I eventually upgrade my phone.