feat(competitions): logo banners on competition grid cards

[shauryagangrade]

What

Adds an optional image field to the competition schema and renders a logo banner on the grid variant of the competition card.

Changes

• Schema + types: image (e.g. "/competitions/xyz.png") added to data/competitions.schema.json and Competition in src/lib/types.ts
• Card UI: grid cards now show a 2:1 logo banner (next/image, object-contain) that links out to the official site in a new tab; falls back to a trophy placeholder when no image exists
• Data: image populated for all 75 existing competition entries across the 15 category files
• Assets: 75 favicon-derived logos in public/competitions/
• Tests: 2 new unit tests (banner renders + links to official site, placeholder fallback) plus a next/image mock

Verification

• npm run validate — all 15 competition files clean
• npm run test:unit — 438 tests pass
• npm run typecheck — clean
• npm run lint — clean
• npm run build — passes

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Project	Deployment	Actions	Updated
study-map	Ready	Preview	Sep 6, 2026 12:00pm UTC