Support for DoT should work with any version of OpenSSL or GnuTLS but for DoH it requires the addition of h2o_socket_get_ssl_server_name() in libh2o (PR in preparation). It's already possible to do HTTP Host header matching for DoH, though.
The corresponding PR to h2o is h2o/h2o#2054. I don't think we need to wait until it is either merged or refused, though, because even if it does not make it we properly detect that the support is not present.
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