Have you heard about Wire? Groups up to 500, when they switch to MLS protocol then thousands, e2e, Swiss based and it has kind of ok UI.
It has a single UI, so it's out. Wire specifically disallows anything 3rd party.
And an Android app that doesn't combine the slowness of iOS and Android would be nice. To be clear - their animations (to me) drag on too long (as one might say about iOS), and UI input takes a noticeable amount of time (which is commonly found on Android apps that aren't well-written).
While this may not be helpful for anyone looking to improve the apps, that's kinda more of the same point - nobody is allowed to make a better client, as it's against the Wire ToS. This is why there's no Matrix bridge.
Found Matrix, happy with it. It likely will adopt MLS, too.
PS: these days swiss based is a bit of a stretch