If you have a product people really like but it doesn't seem like people are aware of it and want to encourage more adoption, you go looking for places to advertise... but the people most likely to want a internal version of SO are the people using SO. That means the obvious place to advertise is on Stack Overflow.

I think it's a bit overboard to make it the focus of the home page rather than a secondary focus. But the homepage can change. It's already changed once.

Lots of companies make the centerpiece of their homepage their big new product. When Teams is better-known, it probably won't need to be so obviously marketed.

I think what makes this so jarring is that the first use of the homepage is for a specific reason rather than to talk about SO's primary purpose. If the page talked about how to ask/answer (something like a short version of the tour page) before it mentioned the other things (Teams, Jobs, etc) would that have been okay?

I don't generally find the homepage to be a stellar introduction to SO.