It doesn't "just work", because it's a HTTP authentication flavour that happens to occur at the Transport layer.
Because it crosses layers like this, HTTP has to know about the transport.
For example, it's possible in HTTP 1.1 to have a page trigger cert auth even though the initial transport didn't use it! This is common for logging on to pages using Smart Cards but leaving an option to use alternate authentication modes.
This was just... abandoned in HTTP/2 (and HTTP/3) as "too hard".
Or more accurately, every authentication mode not used by Google was abandoned and does not work.
I've tried HTTP/2 with products from numerous vendors, and without fail anything Google doesn't use... didn't work.