Don’t most ETOPS certified aircraft have the letters “ETOPS” painted in really large letters on several places on the aircraft?
Not most, ALL are required to have ETOPS. The crew is the last to insure that all ETOPS requirements have been met.
There is a requirement to transmit to Dispatch, after airborne, that operationally the aircraft is good to continue.
This is spelled out in the Operations Specifications cleared by the FAA. There will be a big fine to go along with the many red faces.