At the moment there''s a bug in WebDriver to run Safari on iOS. I've contacted devrels for Safari and filed a Feedback Assistant issue, I hope I can get some help to fix that ASAP. The problem is that you connect your phone to the desktop you need to trust the computer/device. Doing that the computer/device is paired. However even if the phone is paired (you can verify that in Xcode) WebDriver think it is not and cannot start Safari ("device is not paired"). On my iPhone its 100% reproducible on two different Macs (both on Catalina and Big Sur). I've been testing on iPad and I got the same behavior there, however there it works maybe 1% of the times.
I've got response with some workaround but it didn't work. I've also been able to reproduce the problem on iOS 13 so I'll send feedback to them again later today.