No it doesn't! When you use GMail, you understand that Google have some potential sight of your emails and you accept that because that's how it works.
What you DIDN'T sign up for is Chrome, which can see every site you have every visited, sending all of that info to Google as well to perhaps start targetting some different ads at you. I'm sure that would work well if one of your housemates had visited a dodgy site, which then picks up some suspect ads when you are doing online shopping with your girlfriend.
Maybe switch to Firefox and use their accounts toggle feature. It lets you separate out sessions for particular sites. It’s not “chromium” but it works well for what you are asking for as far as I can tell.
>Would you mind to explain how using gmail is fine but having to log in into chrome is not?
Well, I've sort of just accepted that Google has all of my personal data at this point. I trust them with data that I want to explicitly give up for the sake of convenience. Anything I type into Gmail I can accept as becoming essentially public record.
However, that doesn't extend to passively collected browsing data. It creeps the shit out of me that my private browsing history could be associated to my real life identity and other PII by someone at Google.
What you DIDN'T sign up for is Chrome, which can see every site you have every visited, sending all of that info to Google as well to perhaps start targetting some different ads at you. I'm sure that would work well if one of your housemates had visited a dodgy site, which then picks up some suspect ads when you are doing online shopping with your girlfriend.