Where do I update Google account details in iOS13?

I think you're mistaking work accounts with Google ones. This is my work mail setup and my Gmail and Outlook look the way yours do. They don't offer explicit password fields in settings AFAIK. They use web interfaces as overlays, at the time of login.

As in macOS Mojave's mail too, there is no password field, Google is now using Safari.

So if you have changed the password of your Google account, it should automatically notify you and ask for password. But if you want to trigger it manually, try toggling off and on the mail switch from the list.

For a drastic approach(if it's a big mailbox), Deleting it and adding it back will allow you to change the password.