windows new browser is free software?

Unlikely - it will probably be like Chrome and Safari - a non-free browser using a (mostly) free engine.

Tivo, MacOS, and Android were all examples of the same thing. A lot of the datafarms (FB, gOgle etc) use a lot of free code on their servers. In all these case, free code cores are packaged up in forms that end up denying their end users some or all of the four software freedoms. This happens so often we need a term for it. At one point some people used to call it "open core", but the person who coined that phrase now discourages people from using it in this way:
http://ebb.org/bkuhn/blog/2011/03/05/open-core-slur.html

If the phrase "trojan horse" didn't already have an established meaning in computer terminology, it's quite appropriate. PR about the product being "open source" is often used to make it seem more hip and cool, and hijack people who believe they're supporting software freedom into doing unpaid marketing for the company selling it, while slipping in anti-features through the back door. Canonical and Ubuntu are a classic example of this, as a lot of us only realized when the Amazon Lens debacle happened.

Even if Microsoft's new browser is based on "open source" Chromium, it can still be non-free, because Chromium is released under permissive license (i.e. not copyleft).

And don't forget Microsoft's Secure Boot. It not only restricts operating system but also application software, drivers and even documents. It's very possible that Microsoft releases the new browser under a "free" license but prevents user-modified version from running. In such tivoized systems, there is no freedom. Only GPL v3 can defeat tivoization.

You are allowed to take chromium and make a non free software version of it?