Suppose I and my partner want to be able to bookmark something and have it show up on both of our phones. Is there a way to do that without sharing a Gmail account? That seems like a pretty common use case to me that was pretty easy to do before Chrome tied them together.

On Firefox, that use case would be trivial. You just sign all your browsers into one account and then use the web normally like you've always done.

No, my suggestion was to create separate user accounts on the shared computer for each person--i.e., each person logs in to the computer with their own user account. That would make all of the website logins separate for each user, without anyone having to switch profiles in their browser.

However, I apparently misunderstood your problem; you don't want everything separate, you just want gmail separate while still sharing Chrome profiles. You're right that my suggestion won't solve that problem.