Sure, at an obscene price.

You said it yourself.

Extra points if I could host my ebooks and music there and run a torrent client. Extra extra points if I could connect to it from outside my home network (and stream)

To start, if you’re using it to torrent your media then you’re going to want it running in the background because you need to seed your torrents. Aside from it being the right thing to do, keeping a good ratio is necessary to get into good private trackers. And torrents aren’t great for music, at least not in my experience, so you’ll probably want soulseek as well. That also requires sharing in the background. You could buy a seedbox and torrent through that, but if you were going to go that route you could just do everything you’re trying to do through a seedbox instead of getting a NAS, and it wouldn’t take long for the subscription costs to surpass the costs of self hosting.

So now you’ve got qbittorrent, soulseek, Plex, and Kavita or similar for ebooks. What else could you want over time? Do you want to host audiobooks, too? Comics/manga/magazines? Maybe you want to streamline and automate the downloading process. Maybe your mom can’t stream her favorite show anymore so you decide to share your library with her. Maybe you want to be able to search and download anything from any device anywhere, and maybe you want your mom to be able to as well.

Why stop there. Maybe you want to self host your own file and picture cloud storage as well. Maybe Mom’s, too. Maybe you want to start blocking ads on your network at a DNS level. Maybe you want your phone to use your home network even when you’re out and about. The possibilities increase exponentially once you start getting into self hosting.

I don’t want to hear the fans

That being said I have a good number of the above tasks running on an HP elitedesk mini g9 and it stays pretty quiet. The spinning disks make noise though lol

Edit: After reading through the rest of the replies I understand your situation a bit more. I see you don’t want to build something or run it on your current desktop. It’s hard to tell you which way to go without knowing at least your current budget and storage expectations. Because you can get a Synology and it will work out of the box for your needs right now, as someone said, but, you will be throwing money away that could better go towards more storage or compute, and in the end you’re limited to their walled garden. As someone else said, you’d be much better off with TrueNAS as your OS. It all depends how much time, energy and money you’re willing to throw at the problem. That is to say, are you looking for a hobby or are you looking for a solution? In any case, installing Plex on your desktop is the easiest and most common first step. You can set up a small library and test it out, see how loud it gets and how much power it draws if that’s your concern. You will be streaming media to your bed by bedtime. Learn how to use it, then when you figure out your next steps it is easy enough to migrate, or just start over with the wisdom you’ve gained along the way. And YouTube is a good enough resource for this. There’s a variety of steb-by-step NAS builds. And though there are definitely guys on there that don’t know what they’re talking about, if you watch enough NAS building videos you’ll catch on quick enough to the necessary components. Anyway hope that helps.