Fix LinkedIn auth lifecycle

[theotarr]

Summary

• reuse the captured LinkedIn browser session fingerprint for API and realtime requests
• validate stored auth with a bounded single probe that distinguishes expired credentials from transient failures
• propagate typed auth-invalid failures out of sync workers and stop scheduling sync until reauthentication
• centralize LinkedIn request context and add direct lifecycle, timeout, user-agent, and invalidation coverage

Root cause

Cued imported LinkedIn cookies but then sent requests with a different hard-coded client identity. Stored-session validation also treated every request failure as expired auth, while background auth failures lost their type at the worker boundary and kept retrying.

Validation

• thermonuclear review: APPROVABLE, no remaining blockers
• pnpm check:app-quality
• pre-push pnpm check:ci-local
• swift build --package-path native/macos/CuedNative -c release
• 75 test files / 504 tests passing
• locally authenticated and completed LinkedIn sync using the patched runtime

Scope

This PR is intentionally LinkedIn-auth-only and excludes the Chromium packaging changes tracked separately in #39 and #58.