Great, progress at last! 
but unfortunately I don’t have any good guesses where on the phone the issue is. I would still suspect something that filters traffic on the network level like a security tool, etc., but I am blindly guessing. Plus my iPhone knowledge is rather limited because I’m so far an Android user and am still waiting on my iPhone 15 to arrive in the mail 
Thinking … maybe it’s cookies? Are you by any chance blocking cookies in Safari? Or maybe try going to the Safari settings and clearing all cookies with Roon in their name.
My purpose here was just to figure out if it’s really something with the phone that was causing the issue.
Yes, it needs to adapt to larger displays, but as far as I know it should be functional, just too small (it is functional on my Android tablet - haven’t tried it on my iPad, but according to other posts I think it should be functional, too). Adapting to larger displays is on the roadmap: