One of us! One of us! One of us!…
@zeeclor has provided a pretty comprehensive list of things to explore (other than perhaps rickroll… I do wonder if that’s what I think it is 
), and I’m sure others on the forum will be able to cover Jellyfin/Plex/media hosting more generally.
I’ll throw the following less well known ideas out there as other potential interesting projects to host:
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ADS-B receiver. Feed commercial sites such as FlightRadar24 and be rewarded with premium subscriptions, contribute data to non-commercial sites with open data sharing policies (e.g., ADSB.lol), or do any combination of the above. Can always roll your own setup using tools such as readsb, follow the bouncing ball using the instructions from one of the commercial aggregators as a starting point (e.g., FlightAware), or use the excellent ADSB.im project which does all of the heavy lifting for you. I’m not affiliated with any of the sites or projects listed here, but have been messing about with this for well over 5 years at this point using every combination of x86/ARM/MIPS/full sized/embedded/virtualised/VPS/onsite/remote/distributed/indoor/outdoor and so on, so if you’re curious about this area then I’m happy to go through it more. Uses inexpensive RTL2832 based hardware such as RTL-SDR devices, specialised branded devices (e.g., FlightAware Pro Stick, AirNav Radar FlightStick based on the RTL2832), or any old generic thing with an RTL2832 inside if you want to get started with a low cost of entry.
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AIS receiver. Same same, but boats. Distinct from and a different technical implementation, but conceptually similar to ADS-B. I’ve got no experience here but a quick search throws up AIS Catcher as an interesting looking project, and a few other sites where you can feed data such as AISHub. Also uses RTL2832 based devices.
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BirdWeather. Same same, but birds (kinda). Uses a microphone to record and identify which birds are in your area. Comprehensive instructions for Raspberry Pi builds available, but I’m also certain a microphone USB pass through would virtualise quite well into Proxmox. Not dipped my toe into this one yet as I’m trying to resist buying new hardware (microphone, weatherproof boxes, etc).
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Decode weather satellite imagery and create your own archive of images. GOES geostationary satellites stay in a static position (relative to you) so you won’t need to muck around with rotating antennas, etc. No personal experience, yet. Had a brief look at it years ago and there’s a fair bit out there and lots of good resources. A brief search threw up this interesting looking project on GitHub to cover off a nice web interface for decoded images. Easiest entry point is once again something with an RTL2832 in it.
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Set up tvheadend to either decode FTA TV and host local streaming to other devices and make a DIY network DVR for home, or pair it with something like ZeroTier and get some HLB members to test out multicast network video. Adding this one to the list as it’s something that I messed about with years ago for my LAN, and when I saw you had 250Mbit upload I thought it might be a good way to experiment with setting up multicast video as well (or even unicast, for that matter). Even if you don’t go down the route of getting external people involved, it would make a pretty sweet multi-user home DVR setup and supports TV guides, pulling in streams from IP TV, etc. If you want to cover FTA decoding, you’ll require a TV tuner. No guesses as to which one is probably the cheapest and easiest one to get started with (hint: it begins with RTL).
My vote is to either do the very cool looking bird project, or buy a box of RTL2832 based devices to play with.