I was recently told by my manager (large FAANG) that I should never expect my skip manager or above to respond to my messages/emails. I should always book time

I was recently told by my manager (large FAANG) that I should never expect my skip manager or above to respond to my messages/emails. I should always book time on their calendar. After 2 years, this was when I knew that this particular manager was struggling with the same problems in the local working unit and that leadership at the VP-level (externally hired) was totally inaccessible to help make critical decisions. It's a tough job market, but I'm looking more ferociously than ever as of this week.