feat(seo): add discovery infrastructure (sitemap, robots, favicon)

[martyy-code]

Problem statement

The template has no machine-readable hints that help search engines and AI tools discover and index the documentation site efficiently. Specifically:

• No sitemap.xml — Google must discover pages via crawl only. New pages take weeks to be indexed.
• No robots.txt — no directives to crawlers, no link to a sitemap.
• No favicon — adopters see a grey square in the browser tab. Cheap to fix, professional touch missing.

For a public template, every adopter inherits these gaps.

Proposed solution

Add three small route files at the App Router level:

• src/app/sitemap.ts — exports a MetadataRoute.Sitemap built from source.getPages() with each page's URL, lastModified, and priority.
• src/app/robots.ts — exports a MetadataRoute.Robots with Allow: / and Sitemap: <absolute URL>.
• src/app/icon.tsx (or icon.png) — Next.js auto-handles favicon generation.

References:

• https://nextjs.org/docs/app/api-reference/file-conventions/metadata/sitemap
• https://nextjs.org/docs/app/api-reference/file-conventions/metadata/robots
• https://nextjs.org/docs/app/api-reference/file-conventions/metadata/app-icons

Acceptance criteria

• /sitemap.xml returns valid XML listing every page from source.getPages()
• /robots.txt allows all crawlers and references the sitemap absolute URL
• Favicon renders in the browser tab on /, /docs, and any sub-route
• No regressions on existing routes or build

Alternatives considered

• Third-party sitemap packages (e.g. next-sitemap). Rejected — Next.js 16's built-in support is sufficient and avoids a dependency.
• Dynamic robots.txt from a Route Handler. Rejected — robots.ts is the modern App Router pattern and integrates with MetadataRoute.
• Static favicon as PNG asset. Equivalent outcome; pick whichever is easier.

Risks

• A syntax error in robots.txt can accidentally de-index the entire site. Mitigation: validate output in CI.
• Sitemap URL must be absolute — depends on metadataBase from the rich metadata issue.

Related

• Sibling issue: rich metadata (depends on this for absolute URLs via metadataBase)
• Sibling issue: JSON-LD structured data
• Next.js metadata conventions (linked above)