I work in multiple locations with a few computers, it's not just my individual laptop - that's straight forward. But I use Google sheets etc regularly on one or more. It's not uncommon to occasionally forget to log out of this, I'm on human. I never said it was a chrome specific issue. But when I log onto my outlook email it will log me out if I close the browser. For Google I have to manually log out of it, simply shutting the machine down or closing the browser does not do this.
If there is a setting available to change this I'm all ears.
And my point about the passwords is that if someone managed to gain access to your Google password (just one password) then they'd not only have all your other passwords but also where to look for them. I.e. if someone guessed my password for X they wouldn't necessarily know that I had an account with Z to log in... but with this they would.
I'm not bashing I'm genuinely asking a question in case there is a solution, or if it's someone nobody else worries about.
Well this is no different then any password manager in existence. You have a "master password" for your vault and then you have all your other passwords stored. If someone was to login to your PW manager then they would have access to ALL your passwords.
The main thing with PW managers is you are not supposed to allow people to log into them. The Master Password (in this case your Google one) is supposed to be a hard one that only you know / remember. Along with that you are supposed to have a 2nd factor for it as well to ensure they can't just get your password and be in.
So to answer you first question -- I am not worried about it since you have to take some initiative if you plan to use a PW manager. They are amazing and fully worth it but you can't just be lax with it and then wonder how it isn't secure. Security always takes layers + time + sometimes things that aren't the most convenient.
As for your Outlook email it will log you out of the browser... IF... you didn't select the "Remember me" when logging in. Google will do the same thing. When logging in uncheck the "Remember me" but I do agree that I wish Google kept that option when logging in (seems to have gone missing). So for that I would suggest just being very mindful. I value my Google account a lot so I haven't ever run into forgetting to log out since it is a prime thing to do when I am done (especially if on a PC that isn't mine at home).
TBH I would suggest using a real password manager like LastPass or something. What Google is doing is good for most people but if you truly are worried I wouldn't link your Google w/ all your passwords. Also I would highly suggest you get into 2FA for any / all accounts you can if you aren't using it (from what you said earlier it sounds like you are just using PW).