Add comprehensive logging to debug slow job completion

- Add timestamps to prepare.ts completion
- Add timestamps and signal handlers to both MCP servers
- Add start/end logging to update-comment-link.ts
- Add final action completion logging step
- Log when composite action steps complete vs job cleanup

action.yml

@@ -111,6 +111,12 @@ runs:
         ANTHROPIC_API_KEY: ${{ inputs.anthropic_api_key != 'use-oauth' && inputs.anthropic_api_key || '' }}
         CLAUDE_CREDENTIALS: ${{ inputs.claude_credentials }}
 
+    - name: Log before Claude Code
+      if: steps.prepare.outputs.contains_trigger == 'true'
+      shell: bash
+      run: |
+        echo "[$(date -u +%Y-%m-%dT%H:%M:%S.%3NZ)] Starting Claude Code base action..."
+        
     - name: Run Claude Code
       id: claude-code
       if: steps.prepare.outputs.contains_trigger == 'true'
@@ -165,6 +171,13 @@ runs:
         VERTEX_REGION_CLAUDE_3_5_SONNET: ${{ env.VERTEX_REGION_CLAUDE_3_5_SONNET }}
         VERTEX_REGION_CLAUDE_3_7_SONNET: ${{ env.VERTEX_REGION_CLAUDE_3_7_SONNET }}
 
+    - name: Log after Claude Code
+      if: steps.prepare.outputs.contains_trigger == 'true' && always()
+      shell: bash
+      run: |
+        echo "[$(date -u +%Y-%m-%dT%H:%M:%S.%3NZ)] Claude Code base action completed with status: ${{ steps.claude-code.outcome }}"
+        echo "[$(date -u +%Y-%m-%dT%H:%M:%S.%3NZ)] Starting comment update..."
+
     - name: Update comment with job link
       if: steps.prepare.outputs.contains_trigger == 'true' && steps.prepare.outputs.claude_comment_id && always()
       shell: bash
@@ -200,3 +213,10 @@ runs:
         else
           echo "⚠️ Claude Code execution completed but no report file was generated" >> $GITHUB_STEP_SUMMARY
         fi
+        
+    - name: Log action completion
+      if: always()
+      shell: bash
+      run: |
+        echo "[$(date -u +%Y-%m-%dT%H:%M:%S.%3NZ)] Claude Code Action composite steps completed"
+        echo "[$(date -u +%Y-%m-%dT%H:%M:%S.%3NZ)] Waiting for job cleanup..."