Add structured data (JSON-LD) for Home and Solutions pages

[scholarsmate]

Summary
Implement schema.org JSON-LD to improve rich results and SEO.

Scope

• Home page: Website + Organization with logo, url, sameAs social profiles.
• Solutions pages: Product/SoftwareApplication for OmegaMatch, OmegaOMG, OmegaOMG VS Code; include brand, offers (free), operatingSystem, applicationCategory, and repository URL.
• Optional: BreadcrumbList for /solutions/*.

Tasks

• Add a small helper to render JSON-LD safely (or inline via next/script).
• Home: Website + Organization JSON-LD (logo in public/images, site URL, sameAs).
• Solutions pages: Product/SoftwareApplication JSON-LD per page with repo links.
• Validate with Rich Results Test.

Acceptance criteria

• No JSON-LD errors in validators.
• Pages eligible for relevant rich results where applicable.
• Code lives near pages (App Router) and is easy to extend.

Notes

• Coordinate with per-page meta work.

[scholarsmate]

Tracking: #4