I've been using Tampermonkey on android for years, and it worked fine, just like other addons that don't happen to have yet been blessed so that users are granted the privilege of being able to choose to install them.
For reference, to work around mozilla's artificial restrictions, you have to use nightly. Once you activate the debug menu (about firefox > tap logo 5 times) there's the option to set a "custom add-on collection". You can make a custom collection on addons.mozilla.org using a firefox account. The two fields are the last two parts of the URL on your custom collection.
Not only is this very cumbersome (especially if you want to add another addon to your collection and have that propagate to your phone), but it's only available on nightly. And nightly has a nasty habit of breaking. It's not much fun when an update causes it to crash immediately on visiting certain websites; even worse when restarting causes it to try to load the tab that just caused it to crash.
So, it ends up in a dilemma: you can either have a browser that doesn't catastrophically break every few updates; or you can have the freedom to install whatever addons you like. But not both.
And that dilemma is entirely artificial and unnecessary. Mozilla could have a process of verifying that addons work correctly on android and warn if you try to install one that isn't so verified (like how Valve has "Deck Verified" but doesn't stop you installing anything you like). But that's not what they've done, and they don't show any sign of changing their minds.