Google keeps asking me to sign in with my Google Account

If this happened in Chrome, I would understand it, but it happens in Safari. I personally don't believe in trusting my passwords to third-party entities like Google, Facebook or the like except for third-party independent password managers.

I completely agree with you.

Is this popup caused by some plugin or something?

Unfortunately no.

Lots of people misunderstand the underlying reason. Please read this recent Discussion for the sordid details: Google Popup Signing Prompt - How stop it? - Apple Community

Response : Timothy Arends 1 🖊️ Sign in With …

Hi Timothy ,

It's no problem , it's optional for those who wish to use their platform to sign in . It's becoming increasingly popular , not all sites have " sign in with " , Apple does , and here's a link on how to use it , as well as two screenshots of examples .

https://support.apple.com/en-us/HT211687

Timothy Arends1 wrote:

The link you provided was about signing in with Apple, but my question was about a "Sign in with Google" popup.

SteelCityAnne was giving that to you as an example of how Apple has a similar service.

It is unlikely that you will be able to stop those popups to sign in using Google as they are served up by the website.