how to make default torrent handler (.torrent files and magnet links) a certain Transmission Remote GUI URL?
Install https://github.com/transmission-remote-gui/transgui on every mac.
Launch it and input Remote host: that-macs-url, Port: 9091. I found out the hard way that a .local (mDNS) hostname will not work on macOS, due to bugs.
It's up to the application what happens when you click on a magnet link. In Safari nothing seems to happen for me for some reason*, but in Firefox I get the option to browse for an app. For torrent files my best bet would be to right click a torrent file → Show Info → Open with: and change all to open in transgui.

Disable prompting for download options in transgui, and use transgui as the default app in your browser to quickly send torrents immediately to your server with a single click and zero context switching. Update: seems that I lost the feature of zero context switching at some point (transgui 5.16.0 on macOS 10.14.4). Transgui now always steals focus when opening magnet links.
* I believe magnet:-links aren't strictly valid URIs.