Docs: rewrite the examples page around user scenarios

[nerdchanii]

Summary

• replace maintainer-oriented examples framing with user-facing scenario sections
• keep the Local Vite, React Router loader, and Next.js App Router examples while clarifying when to use each one
• remove docs-maintenance wording and copy-paste safety columns from the public examples page

Type

• API
• Runtime
• Testing
• Docs
• Tooling
• Packaging/release

Priority

• P0 - Critical
• P1 - High
• P2 - Medium
• P3 - Low
• P4 - Backlog

Verification

• Tests added or updated
• Typecheck passes
• Build passes
• Docs/examples updated if needed

Release Intent

• Changeset added
• No release needed (docs/project-only or tooling-only and does not affect consumers)

Notes

Related issue: Closes #118

Verification:

• npm run docs:build
• npm run lint

[nerdchanii]

@codex review

Context:

• Issue: Docs: Rewrite examples page for user scenarios #118, milestone: post-v1 stabilization

[chatgpt-codex-connector]

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[chatgpt-codex-connector]

Preserve the provider example anchor

Renaming this heading changes the generated docs fragment from #local-vite-provider-example to #local-vite-app, but docs/agents/agent-context.json still points the provider-backed React app example at docs/public/examples/index.md#local-vite-provider-example. Agents or tooling that follow that metadata now land on a missing/incorrect section, so either keep an explicit old anchor or update the metadata alongside this rename.

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