Automatic merge from submit-queue (batch tested with PRs 41146, 41486, 41482, 41538, 41784)

Switch statefulset controller to shared informers

Originally part of #40097 

I *think* the controller currently makes a deep copy of a StatefulSet before it mutates it, but I'm not 100% sure. For those who are most familiar with this code, could you please confirm?

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