They’re private, internal projects. Regardless of the name, you’re not going to find much useful on Google.

Currently, yes. Elsewhere in this thread the author mentioned they do think of making it open source from time to time.

And looking beyond the current example, there are multiple things called home known by millions of people (the English word and the Google product, and I'm sure there must be more).

When you want to find a Google Home online, do you have trouble doing so due to the apparently ambiguous name?

I like to be able to refer to products by their name, rather than have to name the parent company in order to make clear what I mean.

But the name of the product includes the parent company name. It's called Google Home, not Home.