Do gmail and google search are connected somehow ?

I'm using an email of the company [email protected] but it's gmail access, The question now is, if anyone of the team access my email (because it's shared) Will they be able to see what Did I search in google during the last period ?

Sure

https://myactivity.google.com/myactivity
Google tracks every single aspect of your life if you have connected your account to your Chrome browser