Add Xquik provider and restore Twitter monitor pagination

[kriptoburak]

Summary

• Add Xquik as an optional twitter_monitor search provider.
• Preserve TwitterAPI.io as the automatic preference when both keys exist.
• Wire Xquik credentials through core, CLI, web, and docs surfaces.
• Normalize Xquik results into the existing TwitterPost output.
• Keep the shared retry, timeout, and error handling paths.

Independent Repository Fix

twitter_monitor already returned continuation cursors. Its input could not accept them, so callers could not fetch the next page.

Signed commit 911d7e5 adds the missing input and forwards it to both providers. Regression tests cover both request URLs.

Source & Duplicate Checks

• Verified GET /x/tweets/search against Xquik's published OpenAPI schema.
• Verified TwitterAPI.io's documented cursor query parameter.
• Checked open and closed issues and PRs for competing fixes.
• Confirmed the fork owner is kriptoburak.

Validation

• Node 20.19.5 focused tests: 13/13 passed.
• Node 20.19.5 full nodes suite: 199/199 passed.
• Core build passed.
• Core typecheck passed.
• Docs MCP build passed.
• git diff --check passed.

External Gate

GitHub Actions suite 82764417083 contains 0 jobs and requires maintainer authorization.

Existing Repository Blockers

• npm ci rejects the checked-in Zod lock mismatch.
• Node typecheck reports existing Apify, Google Sheets, and Slack errors.
• Root test and build hit the existing Google Sheets credential import error.
• Root lint starts Next.js's first-time interactive configuration.

No blocker originates in this PR's changed files.