You can certainly get a similar thing working on a Raspi, but you'll likely notice buffering issues. Especially if you try to stream different content to different clients.
Your archive on bigger drives next to it. Problem solved.
If that's not enough use zfs with a nvme cache and add a few more sticks of ram I to it.
Total cost ~€40.50 per month. Hetzner gives you infinite ingress and a few TB egress bandwidth per month. As long as you only give access to your box to family/close friends you'll never hit that cap. And all they need is a Plex account. Then you just invite them and the setup is done, zero technical finnicking for them.
But yeah, RPi is rough because you do need legit CPU to transcode on the fly, which is what Plex does, and the more users the more transcoding power you need.
But Plex is very limited in its encoding capabilities. H265 with HDR is just not supported properly. On top of that, there is just no way to encode H265 in real time (a high quality reencode of a Bluray can take days on top of the line Xeon CPUs). One would be better off downloading a few versions of the same movie; plex supports choosing which version to play.
One feature I haven't seen on any commercial service is the ability to integrate with your IMDb watchlist, and automatically download "Linux ISOs" when they become available.