Hmmm, I never heard of that rule for California and I’m a California voter. I know that you can’t run for two different offices at the same time.
As you know, Adam Schiff is currently running for a US Senate seat and he hasn’t resigned from his House position yet. I assume that he will complete his term and if he wins the US Senate seat, he will sworn in after the first of the year.
I have no idea about other states.