Multiple reports have been seen within ASC complaining of issues connecting an external monitor, via HDMI, subsequent to updating iPads to iPadOS16.1.
You would be best advised to seek assistance directly from Apple Support. You can contact the Support Team using the Get Support link at top-right of this page. Alternatively, you can initiate and manage your support cases using the excellent Apple Support App. If not already installed on your iPad, the App can be downloaded from the App Store:
https://apps.apple.com/gb/app/apple-support/id1130498044
You should also submit a bug report via Apple’s Product Feedback portal. For iPad and iPadOS:
Feedback - iPad - Apple