Desktop's appendLiveSessionProjection built the `user-inflight-<sid>` row from
`inflight.user` text alone, so a background-process completion (or async
delegation result) that was still running at reconnect showed up as a user
bubble even though history would render the same turn as a `process_complete`
timeline marker once it landed. The gateway now ships `display_kind` /
`display_metadata` on `inflight` (#112162); route a typed row through the same
`toChatMessages` projection history uses, keeping the stable id so the
activate/resume reconcile keeps deduping it. `hidden` prompts yield no row.
Genuine user input carries no display fields and renders unchanged, so a user
quoting the marker text stays a user bubble.
Docs: describe the `inflight` display projection in the programmatic
integration guide.
Part of #112144 (with the salvaged #112162 by @KoNit-K).
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