What insurance to pick to minimize actually dealing with insurance

With open season coming up (federal government employee) I am looking to change my insurance. I’ve been a Kaiser member for years, but I’ve officially become fed up with the months long waits for specialist consultations, cortisone shots, and other fairly routine needs. It also takes longer than it used to for providers to respond to messages (my understanding is they are understaffed, so not blaming any provider here, it’s a tough job with too many patients). However - the one thing I love about Kaiser is that all of the payments, billing, etc is all under one roof. I’ve never once been sent a bill incorrectly, nor had anything denied. I also love that I can call an on call doctor at any time.

What plans should I look into to be able to have all of my records centralized in a similar fashion? Or maybe the question is what providers do you all recommend to support this desire (assuming they take multiple plans)? Should I consider something like One Medical? What else should I keep in mind about potentially switching?