"The session has to be fetched from cache/hot memory on every request, right?"

Nope. Let's say you have a rest endpoint that accepts a Pokemon id to add to your collection. If you cryptographically sign a cookie that says "I am this user id" you can assume the request to add the Pokemon to your collection is valid. There's other business logic to perform, sure, but "I am this user" is taken care of for you.

What Google is proposing is the ability to save a long-term cookie that says "I am this user" and a short-term cookie that says "I'm signed in". The requests periodically say "am I still signed in/am I still this user" and the server can periodically (eg not every request) look that up in cache/database.