Please try the following to resolve your issues.

Make sure your MacBook is up to date.  Go to System Preferences>Software Update.  You should be on Mac OS Monterey 12.6.

Make sure your Apple TV is up to date.  Go to Settings>System>Software Update.

Restart your MacBook. Click the Apple icon on the upper left of the Menu Bar.  Click on Restart.

Restart your Apple TV.  Go to Settings>System>Restart.

If you are using Chrome make sure it is up to date.  If you see the update button on the upper right of the browser please select this and relaunch tabs.  If you do not see it, click the 3 vertical dots on the upper right of the browser and hover your cursor over Help>About Google Chrome.  The browser will automatically update.  Make sure that you have as few tabs open as possible - multiple tabs will decrease your performance and over the long term affect the CPU of your Mac.

Try using Safari.

Download and install Mozilla FireFox.  This is a fast browser that is open source and many argue that it is the best browser out there.

Lastly if you are still experiencing issues, please sign in with your personal Apple ID on the Apple TV itself.  Once you do so you can access the App Store and all the apps you have previously purchased.  If the App you want is free (like YouTube) simply click the Get button.