I wanted to solve this problem by creating a super simple web app, which is only about playing piano with MIDI keyboard. Plug and play.
You can also import .mid file and watch it being played. Recently I added recording feature that will capture playback and these recordings can be saved to cloud and exported as .mid or .wav files.
Future plans involve displaying sheet music, and maybe testing how well live streaming keyboard events over websocket would work.
Too bad Safari doesn't support Web MIDI API but I believe that could be solved by creating native iOS / iPadOS application that would listen to MIDI events while forwarding them into web view.