fix(desktop): rebind mounted sessions after ws reconnect

[FalconOrtiz]

Why

After a desktop WebSocket drop (1006), reconnect could leave a mounted pane painted from warm cache while the gateway still held that session on the drop sentinel. Typed input never reached prompt accepted, and a pending approval.pending frame was lost until the user remounted the chat (#101408).

Scope

• use-session-tile-delegate.ts: warm resumeTile always runs session.activate (restores pending_approval); falls through to cold session.resume when activate proves the runtime dead.
• use-session-actions/index.ts: a timed-out / transient warm session.activate falls through to cold session.resume instead of returning on degraded cache.
• Focused tests for both paths.

Out of scope: gateway orphan-reap / transport ownership changes.

Tradeoffs

Warm tile reuse now pays one session.activate round-trip. That matches the primary resume path and is the cheapest way to prove transport attachment.

Blast Radius

Desktop renderer only (apps/desktop). Affects tiled sessions and primary warm reconnect. Safe failure mode is cold resume.

Verification

cd apps/desktop
npm run test:ui -- src/app/contrib/hooks/use-session-tile-delegate.test.ts
# 14 passed, exit 0

npm run test:ui -- src/app/session/hooks/use-session-actions.test.tsx -t "falls through to session.resume when warm activate times out"
# 1 passed, exit 0

Closes #101408

[Enough1122]

AI code review — automated review for reference; please use your judgment.

Overall: Warm tile bindings are rebound via session.activate before reuse: cache warmth is not transport attachment, and after a WS drop the map can be re-seeded while the gateway parks the session on the drop sentinel (#101408).

Correctness:

• apps/desktop/src/app/contrib/hooks/use-session-tile-delegate.ts:rebindWarmRuntime — omit_messages: true + cols: 96 light rebind; restores pending approvals into the prompt store; missing (old backend) and ok both reuse, dead falls through to cold session.resume after deleting the stale mapping. Re-checked after the prefetch await (second warm path), closing the race.
• use-session-actions/index.ts — non-gone errors (timeouts/blips) now drop only the stored→runtime mapping and fall through to session.resume instead of publishing a live-looking warm cache that drops typed input.
• Tests pin activate-before-reuse, approval restoration, dead-runtime cold fall-through, and timeout → session.resume with $activeSessionId landing on the fresh runtime.

Non-blocking nit:

• Every warm reuse now costs one session.activate RPC, and every blip costs a full session.resume; correct trade (a dropped keystroke is worse than an RPC), but reconnect storms will show as resume churn in logs.

Verdict: LGTM.

[FalconOrtiz]

Requesting squash-merge per engineer agreement (2026-09-04): AI-review merge-ready pack; nits non-blocking; no rewrites.

This PR is in the agreed pack with #101523 #101528 #101529 #101530 #101531 #101537 #101544 #101547 #101548 #101549 #101551.

Out of pack (do not block this merge): #101564, #101796/#101091, #101318.