Extract shared sync HTTP helpers: auth headers and unavailable mapping

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Spec: Fowler-style refactoring review (cloud agent, 2026-08-05). Refactor only — no behavior change.

What to change

About ten browser-side client modules repeat the same two blocks:

• the auth-headers builder including the x-walking-thoughts-test-user bypass: lib/sync/client.ts, lib/sync/trash-client.ts, lib/sync/threads-client.ts, lib/sync/split-client.ts, lib/sync/review-client.ts, lib/sync/media-client.ts, lib/enrichment/client.ts, lib/enrichment/thread-view.ts, lib/artifacts/client.ts, lib/push/client.ts — plus hand-rolled copies in components/daily-digest-panel.tsx (digestHeaders) and components/interview-panel.tsx (interviewHeaders)
• the 401/403/503 → { unavailable: true } response mapping

Extract syncAuthHeaders() and asUnavailable(response) (or a tiny fetchSync(path, init)) into one module (e.g. lib/sync/http.ts) and route every client through it.

Out of scope: retry/timeout behavior; the transports' public interfaces.

Acceptance criteria

• One implementation of the test-user header logic and one of the unavailable mapping; all listed files import them
• digestHeaders / interviewHeaders in components are deleted in favor of the shared helper
• mise run lint and mise run test pass