In some vicious unhelpful semantic sense, I guess you can say that there was no loss of functionality. It would be more technically correct to say that Apple decided to make the functionality much harder to access and to further muddy their human interface guidelines.
As others have told you, streaming content from the Mac to AppleTV used to be as simple as clicking on the Airplay icon on the toolbar and selecting your AppleTV device. There were options like whether to mirror or extend the display. There was the option to stop streaming your desktop to the AppleTV.
(ALSO I used to have the Display icon on my toolbar to make it easy to get to controlling my displays, but Apple took that away a few years ago)
With Monterey you now have to open System Preferences, select Displays, and click Add Display and select your AppleTV there.
Unintuitively, when you select an AppleTV in the Add Display menu, the AUDIO will also be streamed to the AppleTV. THIS is where Apple hid the Airplay functionality that the OP was asking about. (and what if you only want the display output and not the audio output to the AppleTV? How do you control that now?)
If you want to switch between mirroring and extending, you have to click on the Display Preferences button to bring up yet another screen.
Once you have added the AppleTV, THEN an icon for displays appears on the Toolbar, but only until you stop using the AppleTV as a second display. To use the AppleTV again, you have to repeat the process in System Preferences.
And how do you stop sending video to the AppleTV? There is no Stop Mirroring option, and there are no checkboxes on the menu, so you just have to figure out that the trick is to click on the AppleTV in the pulldown menu from the temporary displays icon on the toolbar.
Meanwhile, the Apple fan press is crowing about how neat it is to easily make my Mac into a display for an iPhone. As if my $5K Mac's main purpose is to be a peripheral for my phone. I'm not against being able to display from an ios device to a Mac. I just don't see why Apple had to make controlling display output from my Mac so difficult.