AFAIK, HTTP proxy CONNECT HTTP/1.1 requests tunnel a single TCP connection. After any TCP connection is closed, both upstream and downstream connections are closed. Connection reuse isn't possible. Is it possible to make HTTP/2 requests to a proxy to mux multiple tunneled over a single TCP (upstream) connection to avoid the cost of TCP handshake? Does the HTTP/2 standard allow the CONNECT method?
Yes, in HTTP/2 the CONNECT method exists too:
"In HTTP/2, the CONNECT method is used to establish a tunnel over a single HTTP/2 stream to a remote host for similar purposes"