OAuth2 Client Credentials Grant using JWT Private Key

I'm trying to figure out if there's a way to define an OAuth2 security scheme using a signed JWT instead of a client secret.

When defining the security scheme in the following way, the "Available authorizations" in the hosted UI only shows "client_id" and "client_secret" as inputs. In my use case, I'd need it to display "client_id" and something like "private_key", which might be a file-upload button.

components:
  securitySchemes:
    oauth2:
      type: oauth2
      description: This API uses OAuth2.
      flows:
        clientCredentials:
          tokenUrl: https://example.com/oauth2/v1/token
          scopes:
            example.create: Create an example object

Perhaps this would need to be done as a vendor extension or something?