I would not be running to the DMV to update my driver's license.
Seriously, when was the last time you got pulled over by law enforcement?
I would continue to drive as I always have. If a Flock camera tagged my license plate and I got pulled over, I can always claim "profiling" or "discrimination".
I would remain calm and polite. If questioned, I would answer that my driver's license information correctly shows my identity and point out the gold star that indicates it is Real ID-compliant. If pressed, I would state that there is an error in their system and "on the advice of counsel, I am not permitted to discuss pending litigation." The Fifth Amendment guarantees the right to remain silent and not answer questions.
The very worst thing that would happen is I would be ticketed for driving without a valid license, a misdemeanor. By the time I got to court for my appearance, the issue may have been resolved or enforcement blocked. If not, I could always delay the hearing by requesting a jury trial.
(I am not an attorney, and this is not legal advice. This is merely how I would respond.)
Thankfully, I am not in Kansas. My heart goes out to those who are.