feat: add /integrations marketing page (#integrations-404)

[MJ-RWA]

Summary

Fixes the 404 on /integrations — the route was referenced across v2 nav
components but never existed.

Changes

• apps/web/app/(marketing)/integrations/page.tsx — new page with full
  tile grid, category sections, status badges, and CTAs
• apps/web/lib/integrations.ts — typed data file for all 22 integrations
• public/integrations/*.svg — placeholder logos (real brand assets to follow)
• apps/web/app/sitemap.ts — added /integrations entry

How to test

1. npm run dev inside apps/web
2. Visit http://localhost:3000/integrations — should return 200
3. Confirm all 6 category sections render with correct tiles
4. Check badge colors: Live → green, Coming soon → amber, On request → gray
5. Click "Request an integration →" — should open mailto:integrations@useroutr.com
6. Visit /sitemap.xml and confirm /integrations is listed

Out of scope / follow-up

• Replace placeholder SVGs with real brand logos
• Wire "and 50+ more" on homepage logo strip to this page
• Hook "Request an integration" to Typeform if preferred over mailto

Closes: #138

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