Update the gateway's live turn projection after an accepted correction so a warm session resume does not add the stale original prompt beside the persisted correction.
Cover the inference-time correction path end to end and assert both redirect entry points refresh the live user text.
* test(desktop): cover correction resume without duplicate prompts
Exercise a live composer correction, switch away and back before the
response settles, and assert both user turns retain their order and occur
exactly once.
* test(desktop): cover correction warm resume during tool run
Exercise a correction accepted at a foreground-tool boundary, a switch through a persisted session, and the warm resume back. Assert the original prompt and correction remain singular and ordered.