I’ve used a wireless mouse, keyboard and xbox series controller with my Bazzite desktop. I usually use the proprietary Microsoft adapter with my controller and it just works. Occasionally I will have to disconnect and reconnect the adapter so it will pair, but that’s about it. Using bluetooth for the controller works too
With modern iPhones? I haven’t found a way that works unfortunately. Apple wants to keep their users in the apple ecosystem, so this is always going to be an uphill battle trying to work with Linux.
For music I know rhythmbox use to have good apple connectivity, have not seen it work for any of my current devices sadly.
There is a program called blue bubbles that should bring some iMessage functionality over. I have not tried it personally.
https://bluebubbles.app/
Sadly the best thing in my experience is to keep a mac or pc that has iTunes available for most things. Your mileage may vary though and you end up having better results. Good luck!