Should I be using an httponly Cookie or is it ok to use Authorization header with my Web Socket project?

I have a simple websocket project using the Auth0 React library…

If you wire that up with your Auth0 info

spring:
  security:
    oauth2:
      resourceserver:
        jwt:
          issuer-uri: ...
          audiences:
            - ...
app:
  auth:
    client-id: ...
    scope: "openid profile read:transactions"

You should see it work, however, I am following the instructions and instead of a secure http-only cookie it is having me manually inject the tokens in the headers. I am not opposed to this as I have good XSS measures but is that really the only way? Also, if I am passing an access token can I pass the opaque one and then grab the user info using the token in the backend like in the AuthenticationProvider or something?