Hi,
I am on the latest public betas of iOS 16 and tvOS 16.
The Apple TV remote app on iOS doesn't send text you paste into it to the Apple TV anymore, e.g. URLs pasted into the remote app don't transfer into the input field on a tvOS app; normal text input works fine and is transfered without lag.
In addition, when you try to use a saved login which is shown above the iOS keyboard in the Apple TV remote app, after chosing it, it's not even visible in the input field on the remote app (nor is it transfered on the Apple TV input field obviously)... you have to go into the password list from the keyboard in the Apple TV remote app instead for it to work and be shown at least in the remote app input field, but after pressing enter it's then also not transferring to Apple TV into the respective input field.
It's a nightmare when you now have to put in everything manually, like long URLs etc..