When I try to add a new mod file it just opens a small subwindow with the title Add a Mod, which only contains a text field asking for a URL which I can't even copy paste into. How do I actually add mods?
The web/browser versions only support mods via URLs, and the mods generally have to be hosted on the web due to the security constraints in most/many browsers. You can find URLs for the official mods I’ve created, and a handful from the community that I’ve gotten permission to host on my personal website, on the wiki.
As far as not being able to paste into the mod URL textbox, I just tested it on my mobile and desktop on Chrome and it does indeed work. What system and browser are you using?
Do note that the mod support on the web can be a little finicky and unfortunately, you sometimes have to add mods twice for it to stick. This is a timing and caching problem and it works basically 99% of the time on the second attempt. After adding a mod, go back and check the mod settings to make sure it’s there, and if it isn’t, it should work if you add it once more.
I fixed this in Hex’s version of the engine, but I also rewrote the mod support practically from scratch for that game, so I can’t backport it. When I have time, fixing the initial mod loading problem is on my list.