However it seems like only h2 (HTTP/2 over TLS) is supported and not h2c (HTTP/2 over TCP with upgrade handshake) or HTTP/2 with prior knowledge.

It's a bit unfortunate that because of the decision of the browser vendors to support only HTTP/2 over TLS (for valid reasons) now a lot of libraries and tools support only that mode. For lots of other applications HTTP/2 without TLS would be helpful too.