There are several remotely controlled torrent clients, transmission comes to mind. It has web interface and state of the art is that the webpage registers itself as a magnet: link handler so clocking one adds it to the remote server (disclaimer: I don't actually know that that is a feature of transmission. I use a client that is integrated with my router and it has this despite the router not being particularly nice)

I have a similar setup using Truenas to store data. I've setup a VM in Truenas that can access the data via NFS (easier to setup on Linux than SMB).

It's nice to keep all your services contained in one machine, as long as it has enough resources, and will probably consume less power than running another PC.

I use qbittorrent, most people seem to agree it performs better than Transmission. It's accessible from a web interface.

TrueNAS has a feature built in called Jails that allow you to run applications in their own walled area similar to a VM but more similar to a Container. There used to be a section (haven’t used TrueNAS in a moment) where you could easily attain official and community pre-built jails and install them without much difficulty. QBittorrent was in one of those lists. Definitely worth poking around to see if that’s still there.

Another option would be to stand up your own jail and install the program you want on there yourself. Here’s a quick rundown out there that seems to cover the basics you are looking for.

https://cyberon.org/qbittorrent-installation-in-truenas-jail.html

You may be able to run a torrent client on the NAS?

You could do it on the NAS. Qbittorrent is probably the highest-recommended client right now, and it has a web UI that can be accessed from any other device on your network.

That said, I run one of the tiny Thinkcentres as a dedicated torrent and *arrs box. I think I paid $30 for that one, and it has more than enough power for the task.