docs(landing): add a prompt examples page

[vreshch]

Stacked PR. Base is feature/docs-nav-restructure (#97). Merge order: #97 -> this -> the client-pages PR. Retarget to master before squash-merging.

What

A new docs page, Prompt examples (/docs/prompt-examples), placed in the Memory group between "Connect a client" and "MCP tools".

Task-based sections, each with a short intro and a copy-ready prompt in a code block, captioned with the tools it lands on:

1. Save knowledge as you work (memory__write, and memory__edit for appends)
2. Recall context at session start (memory__search / memory__list then memory__read)
3. Keep memory fresh (targeted memory__edit, frontmatter merge, full rewrite when warranted)
4. Organize and prune (read-only audit first, then move/delete with a plan)
5. Cross-tool workflows (write in one client, recall in another - the same account, one memory)
6. Standing instructions (a CLAUDE.md / rules-file / system-prompt snippet: check memory first, save durable decisions, never store secrets)

Why

The docs explain how to connect and what the tools are, but not what to actually type. This is the page a new user copies from on day one, and it is where the cross-vendor story becomes concrete rather than a claim.

How

Authored as a DocPage data module (content/prompt-examples.ts) using the existing p / code / callout block types, registered in registry.ts and nav.ts. Behavior claims match the canonical facts in lib/mcp-docs.ts (literal keyword search, write replaces, edit shallow-merges frontmatter, delete is recoverable, tools only fire on memory-relevant requests).

Verification

• npm run verify green (type-check, lint, format, vitest 48/48, next build - now 44 static pages, the page and its .md mirror included).
• Checked the built production server: /docs/prompt-examples returns 200 and /docs/prompt-examples.md renders the full markdown mirror with the code fences intact.
• Copy reviewed for the house rules: no em dashes, no competitor mentions, no invented flags or UI labels.

[github-actions]

✅ CI - Verify PASSED

Commit: 3ab65ce4bab801d03dbcc5414c514ea028bf0d1b · Branch: feature/docs-prompt-examples

• ✅ Type check
• ✅ Lint
• ✅ Format check
• ✅ Unit tests + coverage
• ✅ Build
• ✅ Landing e2e

🔗 View workflow run