In Safari, when I use AirPlay when streaming a video from a website, all I get is audio audio and a black screen on both devices, my Mac and my TV. I am using AppleTV 4K and a Mac running Ventura 13.3.1. In Chrome, the video plays on both devices.

Hello KM_MacNewbie,

Thank you for using Apple Support Communities. Sounds like you're experiencing issues AirPlaying video when using Safari. If so, we'd like to recommend some steps you can try to isolate and troubleshoot this issue. For your iOS devices & Mac, you're going want to follow the recommended steps listed here: If screen mirroring or streaming isn't working on your AirPlay-compatible device - Apple Support

Just in case, here are some additional steps you can try on your iPhone:

1.) Clear the history and cookies from Safari on your iPhone, iPad, or iPod touch - Apple Support

2.) Close Safari app: Close an app on your iPhone or iPod touch - Apple Support

3.) Restart your iPhone - Apple Support

4.) Install updates that might be available for your iPhone.

This can usually help with unique issues, since updates include fixes. Just in case, this link can guide you through the update process: Update your iPhone or iPad - Apple Support

1.)Back up your device using iCloud or your computer.

2.)Plug your device into power and connect to the internet with Wi-Fi.

3.)Go to Settings > General, then tap Software Update.

4.) If you see more than one software update option available, choose the one that you want to install.

5.) Tap Install Now. If you see Download and Install instead, tap it to download the update, enter your passcode, then tap Install Now. If you don't know your passcode, learn what to do: If you forgot your iPhone passcode - Apple Support

For your Mac, you can also test this issue using safe mode. This step can help isolate possible software related issues: How to use safe mode on your Mac - Apple Support

Apple silicon

1.) Shut down your Mac.

2.) Turn on your Mac and continue to press and hold the power button until you see the startup options window.

3.) Select your startup disk, then press and hold the Shift key while clicking “Continue in Safe Mode.”

4.) Log in to your Mac. You might be asked to log in again.

Depending on your results, follow the steps under “If the issue continues in safe mode” or “If the issue doesn't continue in safe mode”.

We hope this helps out. Thank you for using Apple Support Communities. Take care.

After restarting in safe mode, do what?

"Depending on your results, follow the steps under “If the issue continues in safe mode” or “If the issue doesn't continue in safe mode”. " means nothing when you don't include those instructions.