Does those push notifications mean that Google has linked somehow my laptop and Gmail account?
What is the best way to protect myself from such "guardianship" (if any)?
Probably the websites where you signed up with your Gmail account have sold or leaked users' data to shady people on the internet, so they keep sending emails of the same kind to you in an attempt to grab you as a customer for services they promote, or in other cases they might be trying to hack you by sending phishing emails that if you click, you are going to infect your device with malicious data which will compromise your safety and privacy.
The best way to protect yourself is to use alternative emails when signing up at websites on the internet. Don't use your personal email in these cases. Keep your personal email only for trustworthy essential websites, services, friends, family, job and real life contacts. Avoid all the rest.
I know what I'm talking about, because I used to commit this mistake since a long ago in this crypto environment, so I still receive a lot of garbage emails in a daily basis, including those ones stating they have very intimate and shameful records of mine and that if I don't give the sender some Bitcoins, I'm going to be exposed.