There’s also PikaOS. It’s using Debian mechanics (so apt as the package manager and such), but a modern kernel and their own repos. If you’re more used to this world, might be worth a look. 8 didn’t know how well it’ll handle the controller and specific button inputs from the deck though.
I personally also came from a mostly debian background, but ended up going with CachyOS for my desktop needs (my deck is still on steam os). It’s arch based, and just very polished and well thought out. It has a version specifically for mobile consoles, like the steam deck.
I disagree with those saying that you can’t do a build for that budget, but I would suggest looking into used parts, at least for some things, to improve the result significantly.
Since your system goal doesn’t seem to be storage related, as nextcloud includes storage obviously, but typically isn’t used to house multi-terabyte data sets. So assuming you can make that work for the “future homelab projects” to with dual 500gig NVME as storage. Search for a used mITX board+CPU that can accommodate that (has the slots), and go from there. Things like CPU cooler, if not part of a possible mainboard+CPU bundle, should be selected after the case at that is the limiting factor for it. Didn’t skimp on RAM size if you can (new or used is fine, depends what you can get in your area).
With this list you’re basically done to get it up and running.