Fix inbox thread refresh after sending follow-ups

[IgorWarzocha]

Problem

Inbox can show stale thread state after sending from the inbox composer.

Seen in dev: after replying from the inbox composer, the inbox view can keep showing the old user prompt instead of advancing to the latest message/thread state. There may also be refresh differences between bun run dev and normal dev branch behavior, so this likely needs a proper sync/data-flow pass rather than a visual tweak.

Scope

• Trace how inbox thread data is refreshed after composer.send from the inbox composer.
• Fix stale prompt/latest-message display after a follow-up is sent from Inbox.
• Check whether the inbox selected thread, sidebar inbox list, and underlying desktop thread data agree after send/stop/dismiss.
• Preserve existing composer behavior and optimistic dismissal rules unless they are the cause.

Acceptance criteria

• Sending a follow-up from Inbox updates or advances the displayed inbox thread state instead of continuing to show the old prompt.
• The inbox list and selected inbox detail stay in sync after send, stop, and dismiss actions.
• Refresh behavior is reliable in dev, including bun run dev / Electron dev usage.
• Add or update focused tests around inbox send/sync behavior where practical.

Notes

This came up during the inbox de-cardification pass. Visual cleanup is separate; this issue is for the data/sync bug.