Can't pair via Airplay from iPhone to new Sony TV

I have a brand new 2021 Sony Bravia TV, an A80J, which is completely compatible with Airplay 2 and Homekit. Or should be.

I am unable to get Airplay to work on it, or Homekit. Here's what happens.

I have the TV set up to accept Airplay, with a code needed 'First Time Only.' I open an app which I will frequently want to cast to the TV, GCN+, and start watching a bike race. The Airplay icon is there in the corner, I tap it, it offers me either my AppleTV 4K (which is not on) or the Sony TV. I choose the latter, and a 4 digit code comes up on the TV screen. I enter the code, there's a delay, then...it fails to connect. Often while this is happening the code actually changes. But in any case it seems like the code expires while the phone is beachballing.

So I try Homekit, enable that on the TV, open the app on the iPhone (an 11Pro by the way), choose 'Add an Accessory,' but as soon as I scan in the visual code off the TV, OR enter the number manually, the code actually CHANGES, and I get the error: Unable to Add Accessory, the setup code is incorrect. Which it is...because it just changed.

This is perverse!

What can I do differently?