feat(extension): refine support and build output

[montasim]

Summary

• move the popup Support action into the header and shorten its label
• write the unpacked Chrome extension directly to apps/extension/.output/
• update tests, the support ADR, README, and deployment instructions

Verification

• full repository check passed through the commit hook
• extension formatting, lint, typecheck, 22 tests, and production build passed
• web formatting, lint, typecheck, tests, and production build passed
• extension ZIP generation was verified with manifest.json at the archive root

[netlify]

✅ Deploy Preview for vidquery canceled.

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