Qt for WebAssembly on mobile devices, specifically phones, has lacked an essential feature - support for the native keyboard. It may or may not have worked. If it worked, it did not work very well. The tricky issue is opening the keyboard when needed and closing when it wasn't. There is no simple API for doing that on any platform we target - iOS, Android and Windows.
Emscripten on Android had one other issue - the usual Emscripten input event API was not working. Nothing being typed on the native virtual keyboard was being handled like on other platforms. I found I could utilize the hidden input element that is used to pop up the keyboard, to listen for input characters and then send them to Qt.
As it is, this patch adds support for native mobile keyboard for iOS, Android and Windows on Qt for WebAssembly. (now merged into dev as 66a76a5def46d0e4a330f7130ad440c639b87cf7), too late to make it into 6.3.
Other issues on mobile are memory (as usual). Up until recently, Safari limits browser memory to much less than the other browsers.
Other areas that Qt covers for mobile devices that do not work on Qt for WebAssembly yet are sensors and bluetooth connectivity. Although there is a patch for some sensors support, it has not been merged and probably needs updating. It may not work at all, either.
Any areas you find Qt WebAssembly is lacking on mobile, please report to https://bugreports.qt.io/