Can I extend display of iPad Pro by connecting to a wireless display adapter over Wi-Fi?

Unfortunately not. Mirroring using AirPlay is just as it suggests - in that the iPad display is "mirrored" to the external monitor. However, AirPlay does permit a video stream to be displayed on an external monitor independently of the iPad display.

What you appear to be exploring is the possibility of using AirPlay with Stage Manager. This combination is not supported.

Apple invites submission of comments and feature requests via its Product Feedback portal. If you would like to see a specific feature or functionality in a future version of iPadOS, this would be the most appropriate channel through which to make a request:

Feedback - iPad - Apple

An iPad can be connected to an external monitor/display using:

• Apple AirPlay (wireless mirroring).
• a wired HDMI/VGA connection with an appropriate adapter.
• a direct USB-C wired connection to a monitor/display that supports HDMI Alt Mode or DisplayPort.

You should note that iPad Pro supports connection to precisely one external display. When used with the iPadOS Stage Manager feature, you effectively have two independent screens.