Fix LinkedIn first-page GraphQL variable replay

[Chkhikvadze]

Problem

LinkedIn Sync Now kept failing on newer first-page messaging GraphQL contracts because the extension replayed captured pagination/window values as if they were reusable.

Root cause

The contract capture treated cursor, countBefore/countAfter, and timestamp-like fields as static captured values. For first-page replay this can resend stale pagination cursors or stale message windows, causing LinkedIn HTTP 400s even after the live request contract is captured.

Fix

• Normalize captured count/countBefore/countAfter to first-page defaults.
• Treat cursor-like variables as optional runtime cursor metadata and omit them for first-page sync.
• Treat created/delivered timestamp variants as runtime timestamps.
• Redact cursor-like values from operator diagnostics.
• Add Attempt Auth: cookie import guidance + /auth/check endpoint #11 coverage for stale cursor omission and safe diagnostics.

Validation

• uv run pytest -q → 425 passed
• node chrome-extension/test_background.mjs → 221 passed, 0 failed

Known gaps/blockers

This does not bypass LinkedIn auth/session expiry. If /voyager/api/me is redirected/rejected or the browser is logged out/challenged, the operator still needs to refresh the live browser session.

Production expectation

Safe to review/land as a focused extension replay hardening fix. It changes only reusable GraphQL contract rendering/diagnostics and does not replay or store cookies, authorization headers, CSRF values, or raw cursor values.