I am getting the “Accessory Not Supported” message on my iPad Pro, despite the fact that there is no accessory connected to it.

Are you using an Apple Smart (folio) keyboard?

This alert is typically characteristic of a faulty folio keyboard. The electrical connections that pass though the flexible fabric hinges typically fracture - this usually resulting in errors and/or the on-screen notification that you see.

The Smart folio keyboard is not repairable. The only remedy is replacement of the keyboard.

Here's the support information covering that error:

If you see an ‘Accessory may not be supported’ alert - Apple Support - https://support.apple.com/HT208277

but since you have nothing connected I think you'll end up having to contact Apple as the situation described halfway down recommends.