docs: sync counts and regenerate pages for product team expansion

Update all documentation to reflect 177 skills, 254 tools, 357 references,
16 agents, and 17 commands. Add 4 new skill pages, 1 agent page, and
2 command pages to MkDocs site. Sync Codex (156) and Gemini (218) indexes.

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

docs/agents/index.md

@@ -1,13 +1,13 @@
 ---
 title: "Agents"
-description: "All 15 Claude Code agents — multi-skill orchestrators across domains."
+description: "All 16 Claude Code agents — multi-skill orchestrators across domains."
 ---
 
 <div class="domain-header" markdown>
 
 # :material-robot: Agents
 
-<p class="domain-count">15 agents that orchestrate skills across domains</p>
+<p class="domain-count">16 agents that orchestrate skills across domains</p>
 
 </div>
 
@@ -73,6 +73,12 @@ description: "All 15 Claude Code agents — multi-skill orchestrators across dom
 
     Product
 
+-   :material-lightbulb-outline:{ .lg .middle } **[Product Analyst Agent](cs-product-analyst.md)**
+
+    ---
+
+    Product
+
 -   :material-lightbulb-outline:{ .lg .middle } **[Product Manager Agent](cs-product-manager.md)**
 
     ---