docs: update factory GitHub mention to @warp

[warp-agent-staging]

Summary

Updates the canonical Warp Factories GitHub integration docs to use the new production @warp mention. The distinct @warp-agent invocation for non-factory GitHub agent runs remains unchanged.

Source product change: warpdotdev/warp-server#17823

Changes

• Replace @warp-factory with @warp throughout the factory GitHub integration guide.
• Update the GitHub row on the factory connection overview.

Verification

• python3 .agents/skills/style_lint/style_lint.py --changed — passed with 14 pre-existing unrecognized-term warnings.
• python3 .agents/skills/check_for_broken_links/check_links.py --internal-only — passed; 4,149 internal links checked, 0 broken.
• Compression contract checks passed for factories/integrations/github.mdx as procedural content and factories/connect-your-factory.mdx as feature documentation.
• npm run build — passed after npm ci; Astro built 386 Markdown docs.
• trunk check — unavailable because Trunk is not installed in the environment.

Unverified claims

• Production availability — the source product PR is still open and draft. Merge this docs change only after the product change ships.

Documentation risk

Risk: engineering-review-required
Rationale: Changes the documented GitHub integration invocation to match the product handle rename.
Source files consulted: warp-server@0ee78682813c50df18f3d49ca44547848d6dbe53: config/prod.yaml, config/github.go, client/packages/factory/src/pages/FactorySettings/DeclaredIntegrationRows.tsx
Engineering review status: pending
Docs override: none

Co-Authored-By: Oz oz-agent@warp.dev

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Project	Deployment	Actions	Updated
docs	Ready	Preview	Sep 18, 2026 3:12am UTC

[warp-agent-staging]

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@hongyi-chen

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[warp-for-oss]

Overview

This PR updates the factory GitHub integration docs to use the new @warp mention while preserving the separate @warp-agent wording outside the factory flow.

Concerns

• No blocking issues found in the changed documentation. The PR body already calls out the release-ordering risk: merge after the production handle change ships and the required engineering review is complete.

Verdict

Found: 0 critical, 0 important, 0 suggestions

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