I keep reaching for Control Center while the iPhone is on the Mac. Flashlight, Focus, a quick Wi-Fi toggle. The swipe that works on the phone does nothing in the mirror.
That is not a bug in your window. Apple never mapped that gesture onto the Mac chrome.
On macOS 27 or later
Focus the iPhone Mirroring window. Press Command-4.
That is the shortcut Apple now documents. Command-1 is Home. Command-2 is the App Switcher. Command-3 is Spotlight. Command-4 is Control Center.
If Command-4 does nothing, you are not on macOS 27 yet.
On older macOS
Leave the phone where it is. Swipe down from the top-right corner on the iPhone itself.
Mirroring stays up. Control Center opens on the phone. You use it there.
It will not draw in the Mac window. Toggles still apply to the iPhone. You just cannot click them from the trackpad.
Same limit for Notification Center. Same limit for the Lock Screen. Swipes from the top of the iPhone screen never made it into the first versions of the feature.
Why the Mac window stays empty
Control Center is a system overlay, not an app. Early iPhone Mirroring forwarded taps and Home. It did not forward those overlays. Apple added the keyboard shortcut later. The overlay still belongs to iOS.
So if you only have the Mac in front of you and you are on an older OS, you pick the phone up for that one swipe. Then you put it down again.