how do i connect my apple TV to my Macbook Pro?

• You cam connect them wired by HDMI, using the TV screen as monitor.
• You can AirPlay over the home network, from the Mac to an Apple TV box that is connected to the TV.
• You can AirPlay over the home network, from the Mac to an AirPlay 2-enabled TV.
• You can use Home Sharing to get media from the Mac on the Apple TV box, over the home network.
• You can user third party solutions similar to Apple’s Home Sharing.

Use Home Sharing to share media from a computer to other devices - Apple Support

Use AirPlay to stream video or mirror your device’s screen - Apple Support

Homesharing is useful because all of the media on the Macbook (music, videos & photos) can be accessed by the Computers app on the Apple TV. The Macbook is effectively a media server for the ATV. I use iTunes on a Mac running Mojave for this since it supports all types of media. Catalina & Big Sur also support Homesharing but sharing is a little more complicated.