Retire Sonar cookbook content and repair docs sync

[andrewmadson-pplx]

Motivation

Public Sonar support ends September 27, 2026, but the cookbook source still publishes Sonar-only examples and guides plus an unmaintained community showcase. The source-to-docs workflow has also stopped syncing: its actions violate the organization SHA-pinning policy, it writes to the wrong destination, and the source and published trees have drifted.

What changed

• Remove all 26 Community Showcase pages, the six Sonar examples, the four Sonar guides, and assets used only by that content.
• Add SONAR_MIGRATION_INVENTORY.md, accounting for all 41 audited pages with stable recovery links and the source-grounded rebuild ranking: 8 rebuild-first pages, 5 rebuild-later showcases, 23 archive-only pages, and 5 retained pages.
• Preserve equity-research-brief, model-comparison, search-news-monitor, langchain-vc-memo-agent, and multi-provider-orchestration because they already use the Agent API or Search API.
• Reconcile every retained non-Sonar recipe from api-docs into this canonical source, including the Finance Chart, SpaceX briefing, and managed-connectors investigation Agent API examples, and correct links to the public perplexityai/api-cookbook repository.
• Store the managed-connectors screenshots in the cookbook static tree so future full syncs preserve the tutorial and its assets.
• Repair the sync workflow with SHA-pinned actions, the docs repository's pnpm/Node 20 toolchain, the correct docs/cookbook destination, static-asset syncing, and navigation/gallery regeneration.
• Remove showcase contribution instructions and stale Sonar recipe listings.

The coordinated published-docs cleanup is ppl-ai/api-docs#783.

Impact

After the coordinated docs change merges, the published cookbook will contain only Agent API, Search API, and Embeddings material. Future changes merged here will again publish the complete cookbook tree and regenerated navigation/gallery data to api-docs.

Merge api-docs PR 783 before this PR. This change enables the repaired push workflow, so landing the published-docs cleanup first ensures the initial canonical-source sync sees an already-matching cookbook tree.