So, unless they’ve made changes since I posted this a few months ago:
AWX doesn’t really support OCP out of the box due to the random UID’s that each namespace runs under. My solution was to build my own AWX images, but I think you can change the SCC to allow AWX pods/ServiceAccounts to runAsUser: type: RunAsAny
For me, the latter wasn’t approved by management, so building from scratch was the only option.
Anyways, I can’t say for certain that this will fix your Web Socket issue specifically, but it may fix other weird bugs/quirks or otherwise wonky behavior.