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Turns out this is harder than it should be.
First of all, you need to run Fennec (from F-Droid) and not Firefox (from Google's Play store), and you need to enable debug mode (which is incidentally a requirement for Firefox sync using a custom server).
Note that even if you have previously enabled Firefox sync using a custom server, you must re-enable debug mode again for the custom add-on collection setting to become visible.
Now you will find a section called Custom Add-on collection in the Fennec settings.
Create your own custom collection by going to https://addons.mozilla.org/en-US/firefox/collections, login using your Firefox account (you have to create a Firefox "profile", whatever that is).
My add-on collection: ID: 17175532, name: fennec.
Fennec will quit automatically at this point. Restart it, and now you can install any of the add-ons in your collection.
Side-note: it's too bad that Mozilla forces us through these hoops to use extensions on Android. I hope this becomes easier in the future.