Airplay from MAC to Ipad not working - screen blanks on MAC

Just to clarify: Sidecar can be used as a mirrored screen or as an extended screen.

Mirrored means that the iPad shows exactly what the main screen (Mac) is showing. Basically a duplicate monitor.

Extended means that the iPad shows a second/separate/independent screen alongside the Mac's screen.

Usually the extended mode is chosen by default. It's expected that a window (the browser in your case) disappears from the Mac when moved to the Sidecar's screen.

When you said "blank" Mac screen I understood that the Mac's screen turns off (black color – showing nothing). If you simply don't see the moved content on your Mac because you moved it away on the iPad's extended screen then it's a normal behavior.

In your case, after filling the form with Apple Pencil on your iPad, you can drag back the browser to your main Mac screen. The mouse pointer moves seamlessly from one display to the other when used in extended mode.

When Sidecar is active, in System Preferences -> Displays you can choose how the iPad has to behave: mirrored or extended. The Sidecar's screen position (either on the left or on the right of your main screen) can be configured as well.

Sorry if I just described obvious concepts.

Is it the first time you experience this issue?

The Mac's screen should go blank only for a few seconds (1-2) during the "handshaking" process. What about the iPad: does it show at least the extended screen as expected?

I assume you have already checked out the system requirements mentioned in the official Apple support pages:

Use an iPad as a second display for a Mac - Apple Support

Use your iPad as a second display for your Mac - Apple Support

AirPlay from Mac to iPad? Are you sure? They other way around is possible: from iPad to Mac (with new Macs).

Ah, Sidecar, now I get it.

Have you tried through a cable (USB-Lightning)?

I'm glad it helped.