test(extension-chrome): extract background-core for unit coverage

[paperhurts]

Summary

Pulls the maybeReconcile + pollRemoteOnce algorithm out of background.ts into a new src/lib/background-core.ts with dependency-injected now, lastReconciledAt, storage hooks, and a runReconcile callback. The new module is fully unit-testable; background.ts becomes a thin wiring layer that resolves the deps and passes them through. Live behavior is preserved — same storage keys, same constants, same error-classification rules.

TDD log

• RED: wrote 11 tests in test/background-core.test.ts against a module that didn't exist. Watched them fail at import resolution — the right failure mode for "this module hasn't been created yet."
• GREEN: created src/lib/background-core.ts exporting runMaybeReconcile + runPollRemoteOnce. All 11 new tests pass. Existing 72 still pass (83 total). Refactored background.ts to call the new functions; e2e and unit suites remained green throughout.
• Hiccup: initial Partial<GitHubClient> typing in the test was too strict for the generic methods. Switched to any to match the existing fakeClient(over: any) pattern used in other test files.

Coverage added

• 1-hour reconcile throttle (early-return when now - lastReconciledAt < interval)
• RECONCILED_AT stamp + lastError clear on success
• lastError persistence with kind: "auth" on GitHubAuthError
• lastError persistence with kind: "unknown" on other errors
• No RECONCILED_AT stamp on failure (so retry runs next cold start)
• read() vs readIfChanged() routing by etag presence
• Early-return on 304 (null result) — no apply, no etag write
• applyRemote + etag write + lastError clear on success
• Silent swallow of GitHubNotFoundError in poll (no lastError)
• Auth-vs-unknown classification in poll lastError

Test plan

• pnpm test 83/83 (11 new for this PR)
• pnpm typecheck clean
• pnpm build clean
• CI green

Closes #4