I'm not sure I will be of much help. My TV is a LG and is showing under Screen Sharing just like it did under the old AirPlay icon.
I tried to look up your TV for answers and did find this article about having to accept a privacy policy on the TV before it will work. I know that you said it worked before, but maybe there was an update on your TV that added the privacy policy.
https://www.sony.com/electronics/support/articles/00260396
My TV also appears under the Home app as it is HomeKit compatible and I believe your Sony would also be HomeKit compatible. I can turn it off/on in the Home app and also set the input of the TV to AirPlay which brings up the Airplay settings on my TV. I don't think the TV needs to be added in the Home app for Airplay to work, but was wondering if you had added yours there as well.
You probably already know this, but the TV and Mac need to be on the same Wi-Fi network. Was there a change in the network for either device?