200’000 tracks is probably pushing it a bit for a 2014 Mac Mini.
One thing you can try is, assuming your drive is NOT a fusion drive, start by replacing the SATA drive by a SSD. This is a little bit involved, but it’s $150 for a TB. If it fails, you’re out a bit of time and $150.
The next stop is likely neither a new Mac Mini nor a new NAS. It’s getting a dedicated Roon machine.
Here again, it depends on how much you’re willing to spend, and how comfortable you are with a screwdriver. The easiest is getting a Nucleus from a local dealer.
I’ve broken the other passive options down here here, if you find better, please let others know. There’s also Small Green Computer, but their stuff, while really well supported, isn’t ROCK, so there’s always the (remote) possibility something might break at some point. One advantage of the HDPlex case is you can conceivably put a really big 3,5" drive into it, house your library there, and have your NAS back it up once a day or something.
If you want a NAS, a nice option, assuming again that you’re OK with building yourself, is UnRaid. Given the size of your library, you probably want at least a recent i5, if not i7, class processor, and that’s neither going to be cheap, especially if you buy pre-built, nor run run particularly cool. The advantage of UnRaid over FreeNas and others is that it spins down the drives it’s not reading or writing to, so that makes it both more energy efficient, and less noisy.
If you’d like something passive and silent there, you can probably have a-tech fabrication build it for you (their page is very outdated. Assuming dual parity, you could hold up to 28Tb of storage in one of those). This would not be cheap. but I haven’t heard of anything else quite like it.