Question about browser security

(Apologies in advanced if this is the wrong place to ask)

A friend and I were having a discussion as to whether or not the following situation is technically possible.

Consider the following scenario.

Say someone logs into their work gmail account and then logs into their personal gmail account. So now we have an internet browser open with 2 gmail accounts simultaneously logged in. Is it now possible for the company for which said person works for to see activity from their personal gmail? For instance, if the personal google drive has pictures/videos, can the persons work company see those? Can they see website activity/history? What about google colab stuff? stuff like that.

My friend has a separate gmail account which he sends himself his own artwork and personal project ideas, stuff like that. He gets paranoid of people seeing stuff that he hasn’t perfected or just personal stuff in general.

My view of the situation is simple. If that was allowed, that would be a massive security breach however, I would love to hear from people much more knowledgable than me.

Thanks!