How many TVs can use Airplay at one time

What you're asking isn't entirely clear to me. You can only use AirPlay from one single device (iPhone, iPad, Mac) to another single Apple TV device at a time.

If you're asking about something else, please explain. Be sure to clarify if you mean an Apple TV device, the Apple TV app or an Apple TV+ subscription.

See here for more information:

Use AirPlay to stream audio and video on Apple TV - Apple Support

If you have a smart TV or streaming device in the bedroom that supports the Apple TV app, you can log in with your apple account and access your subscriptions like Apple TV+ there too.

Airplay would have nothing to do with that.

AirPlay, mirrors your iPhone, iPad or Mac to a TV or supported streaming device. You can use Airplay with any compatible device at any time as long as your iPhone, iPad or Mac is connected to the same Wi-Fi network as the smart TV or streaming device.