iPad Pro 4th Generation can’t use WIRED headphones of any kind. Even with adaptor.

Have you updated your iPad to iPadOS 17.4/17.4.1 ? If so, these versions appear to have some issues with some USB-c devices.

You might be well advised to seek assistance directly from Apple Support - as they may wish to record and escalate as appropriate. You can contact the Support Team using the Support link at top-right or bottom-left of this page. Alternatively, you can initiate and manage your support cases from Apple devices using the excellent Apple Support App. If not already installed, the App can be downloaded from the App Store:

https://apps.apple.com/app/apple-support/id1130498044

Apple also invites submission of comments and bug reports via its Product Feedback portal. For iPad and iPadOS:

Feedback - iPad - Apple

If submitting a Bug Report, ensure that you include details of your iPad model and installed version of iPadOS within the body-text of your report. Don't rely upon the pick-list - as this rarely includes the current versions.

Does selecting Settings --> Sounds --> Headphone Safety --> USB Audio Accessories --> Forget All USB Audio Accessories and reconnecting the headphones resolve anything?

That's all that occurs to me.