fix(core): make inbox reordering durable and atomic - #44858

Correctness follow-up to #44683: replaces its existing enqueue/cancel queue-rewrite workaround with one durable, atomic inbox reorder operation. No new desktop UI is introduced.

Durable inbox reorder

Adds POST /api/session/{sessionID}/inbox/reorder with { inboxIDs: string[] }.

• Publishes one durable reorder event only when queue order actually changes.
• Preserves stable inbox IDs, payloads, timestamps, and immutable admission sequences.
• Adds indexed nullable execution-order storage without backfilling existing rows.
• Preserves original admission order for steers and movement controls.
• Keeps queued synthetic inputs stationary and rejects invalid permutations or compaction/movement barriers.
• Never wakes a stopped session.

Correctness improvements

• Existing drag reordering becomes one atomic request instead of cloning and cancelling queued prompts.
• Existing position-preserving edits replace only the edited prompt, leaving unrelated prompt IDs unchanged.
• Reorder events propagate to the existing web client, full TUI, and mini TUI without adding new controls.
• Public clients, protocol OpenAPI, and API documentation are regenerated.

Verification

• Focused core coverage validates stable identities, admission sequences, indexed query plans, actual promotion order, steer/control ordering, stationary synthetic input, no-op suppression, and transactional rejection.
• Client tests validate the HTTP contract and live queue propagation.
• Existing browser tests verify the same desktop interactions now avoid cloned admissions and unnecessary cancellations.
• 96 focused core tests, 102 full/mini TUI tests, and all repository typechecks pass.

Depends on #44683.