It’s exceedingly rare, but there’s one case where a game can disappear from your Steam library: keys.
Game developers/publishers have the ability to revoke keys at any point, and that can result in games disappearing from your library.
I’m yet to hear of Valve themselves making a purchase inaccessible, but I have had keys get revoked. For example, free Gleam keys that add shovelware to your library.
Even games that Valve banned from sale on Steam can be activated and added to your account using keys. I believe that people who purchased the game also get to keep their purchase even if it’s later banned from sale.
No reputable registrar requires you to run an executable on your machine. JavaScript is as far as it’ll get.
I’m sure many registrars work without JS, but if I had to be sure of any one in particular, it’d be Njalla. They even have an onion site and accept monero, so they almost certainly function without JS.
Since you’re new, I’d recommend just using the old PC to start and get comfortable. Once you’re sure you want to invest some money, you can either build it buy yourself something more energy efficient if you’re super concerned about that.
As for the best OS, just any server OS will do. I run Rocky Linux which is a RHEL derivative, but you can also try TrueNas or anything else you want. Even Windows Server would work if you wanted to go that path.
There are many paths you can take, and which you go down depends heavily on personal preference and the desired use of your system.