If you had a solution, you would have offered it. There isn’t one. The Roku people have been sweeping this under the rug since it started. I’m sure they’ll fix it someday. In the meantime, just keep letting people think the problem is on their side.
A few posts on here does not indicate for this millions of users that successfully are using mirror for Apple AirPlay. I own an iPhone 13 pro and I have zero issues adding my phone to my Roku TV airplay and I can also mirror it. My girlfriend has an iPhone 8 and she mirrors her phone to her Roku also
There is a problem with ROKU software version 1.5.0, Build 4208-50 December 11, 2021 10:07 pm
As with others, I have not been able to screen mirror my iPhone XS under any of the Apple iOS versions during these months—currently iOS 15.4.1
So after these months of struggle, and even trying an ad laden ROKU screen mirroring app (the app did enable mirroring but the display was substandard and highly annoying with frequent pop-up purchase suggestions), I decided to try one more time to connect through the standard process. The ability to screen mirror was the reason I purchased my 3810X - ROKU Streaming Stick + in the first place!
Finally success after a few trys to start AirPlay via Settings>AirPlay and Homekit Settings and restarting my Roku Stick one time.
Previously the ROKU AirPlay splash screen would flash and then the display would go dark for an extended period of time until it ultimately returned to the ROKU Settings menu.
My successful attempt came after the following sequence: ROKU AirPlay splash screen flashed—display went dark—AirPlay splash screen flashed a second time and went dark again—and then the AirPlay and Homekit Settings page was displayed and there I could Turn ON AirPlay, which was OFF by default.
After that my iPhone Screen Mirroring menu was populated with the ROKU Streaming Stick option. Tapping on that worked as it should have, and the Screen Mirroring/AirPlay connection was established.
After that I succeeded in likewise connecting another iPhone 10 without the least trouble.
Conclusion: The problem was that the ROKU AirPlay and Homekit Settings page was not being displayed—therefore AirPlay could not be turned ON at the ROKU end of things.