Have you considered self-hosting? If so, there are a couple of options, such as Calibre-web.

I have been running it for several weeks now and haven’t had any problems. I still use Firefox for things that don’t work well in a Flatpack environment, and Firefox works and syncs as expected. I don’t use a Start page or sync open tabs though.

Utterly outrageous

Have you had a look at binhex’s privoxyvpn docker container? Sounds similar to what you’re looking to do.

Plex can do it, but I assume you need a Plex Pass. I haven’t used the feature myself.