feat(mobile): show a thread's pair on a phone and keep executors out of its lists

[rynfar]

What

The mobile app now shows a thread's pair, and keeps executors out of its thread lists.

• A paired thread shows a notice above the composer: "Paired with · ", the executor's own line of activity when it has one (a plan step while running, the error when failed), and Open executor, which pushes the executor's thread. It renders nothing while the pair is off, so an unpaired thread looks exactly as before.
• The home list and the navigation sidebar no longer list pair executors. They are reached from their lead.
• The phase wording ("Waiting for a brief", "Working", "Needs your approval", …) moved from the web Pair control into client-runtime/state/pair.ts, with pairStatusLine, so web and phone say the same thing.

Turning a pair on or off from the phone is not in this change.

Verification

• vp test run on packages/client-runtime/src/state, apps/mobile/src/features and the web Pair control tests: 1345 passed. Four tests were written first and seen failing: the shared wording, the status line, and the notice's content, accessibility label and empty rendering.
• Typecheck @t3tools/client-runtime, @t3tools/mobile, @t3tools/web: 0 errors. Format and vp run knip:check clean; no new lint warnings.
• Not run on a simulator or a device.

How it was built

Through pair mode on a real install: Claude lead, Antigravity executor, one shared worktree, three test files protected (checked 3, changed []). One executor turn, no corrections.

Part of #622.

Model: Claude Fable 5.1 (lead) with an Antigravity executor, paired in Pylon via the Claude Code harness.

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[vercel]

Deployment failed for project pylon-marketing with the following error:

Resource is limited - try again in 24 hours (more than 100, code: "api-deployments-free-per-day").

Learn More: https://vercel.com/pylon-code?upgradeToPro=build-rate-limit

[github-actions]

Thread transfer impact

✅ Thread transfer remains within every enforced ceiling.

Provider	Metric	Main baseline	This PR	Impact	PR ceiling
Codex	Total thread wire	13.9 KiB	14.0 KiB	+14 B (+0.1%)	15.1 KiB	✅
Codex	Thread snapshot wire	7.2 KiB	7.2 KiB	+2 B (+0.0%)	7.3 KiB	✅
Codex	Live turn WebSocket wire	6.7 KiB	6.7 KiB	+12 B (+0.2%)	7.8 KiB	✅
Codex	Live turn WebSocket decoded	58.0 KiB	58.0 KiB	0 B (0.0%)	66.4 KiB	✅
Codex	Live turn messages	9	9	0 (0.0%)	21	✅
Claude	Total thread wire	13.9 KiB	14.0 KiB	+14 B (+0.1%)	15.1 KiB	✅
Claude	Thread snapshot wire	7.2 KiB	7.2 KiB	−2 B (−0.0%)	7.3 KiB	✅
Claude	Live turn WebSocket wire	6.7 KiB	6.7 KiB	+16 B (+0.2%)	7.8 KiB	✅
Claude	Live turn WebSocket decoded	58.9 KiB	58.9 KiB	0 B (0.0%)	66.4 KiB	✅
Claude	Live turn messages	9	9	0 (0.0%)	21	✅

Baseline: 404c4a3 · PR result: 6dc8163 · Source CI: success

Scenario and decoded snapshot size

10 historical turns, 5 command tools per turn, 878.9 KiB retained MCP result per historical turn, and a 1.05 MiB retained result in the measured turn.

• Codex decoded thread snapshot: 115.7 KiB
• Claude decoded thread snapshot: 116.4 KiB

Updated in place by a trusted workflow. PR artifacts are strictly validated and never executed.

[rynfar]

Merging with the Vercel preview check red: build-rate-limit (#655), from a run that started before #662 taught Vercel to skip builds that do not touch the marketing site. Every code check is green.