So to be clear, you want Mitch to check if there’s a link to F-Droid on a game’s page, and if so, redirect the user to F-Droid, instead of simply installing it? That would make things more confusing, not less. Not to mention the added code complexity.
I’ve had Mindustry on my phone for quite a while now with numerous updates received through Mitch, and F-Droid never seemed to have trouble with this. I might be wrong but I’m pretty sure F-Droid is smart enough to handle these use cases, as it also often co-exists with Google Play, Aurora Store, and other apps. If not, then as far as I’m concerned, that’s F-Droid’s problem. I know there is a way to check which “app installer” was responsible for installing an app.
On the other hand, most Mitch users probably also have F-Droid installed, so they don’t really need Mitch to perform updates of the games.
The main F-Droid repo can be slow to update. Also certain features might be removed to meet their policies. (granted, these “features” might be things like Google Analytics, but still, in general we can’t assume that the F-Droid version will be equivalent to whatever’s on itch.io)