Finally got around to setting up a local Jellyfin server, then setup Tailscale to access it remotely while I'm out.
Setup was super easy — way easier than I anticipated — including the basic setup of Tailscale.
Look out for an option to receive all data they have stored on you. It might take a few days until they have your collection ready but you will receive a nice machine readable data set of what you've watched. It may require some post-processing depending on how crappy their internal data model is. Did this for Netflix and the result was very workable.