Technical info: Looking at a Wireshark trace, I see that the TLS ClientHello message sent by URLSession does not include the "session_ticket" TLS extension. The presence of that extension is needed to tell the server that ticket-based session resumption is supports, so the lack of that extension is preventing the server from ever replying with a ticket.

We are using the older HTTP/1.1 protocol, but with servers that support TLS 1.2. The version of HTTP shouldn't matter since the TLS (formerly SSL) session is established before the HTTP layer of the protocol starts. TLS is a lower-level protocol than HTTP, and the version of TLS used (and its negotiated features) should be independent of the version of the higher-level HTTP protocol.