feat: add Agent SDK support with USE_AGENT_SDK feature flag (#698)

* feat: add Agent SDK support with USE_AGENT_SDK feature flag

Add a feature-flagged code path that uses the Agent SDK instead of
spawning the CLI as a subprocess. When USE_AGENT_SDK=true is set,
the new SDK path is used; otherwise, existing CLI behavior is unchanged.

Changes:
- Add parse-sdk-options.ts for parsing ClaudeOptions into SDK format
- Add run-claude-sdk.ts for SDK execution with query() function
- Update run-claude.ts with feature flag check at entry point
- Update update-comment-link.ts to handle both cost_usd and total_cost_usd
- Add @anthropic-ai/claude-agent-sdk dependency

🤖 Generated with [Claude Code](https://claude.com/claude-code)

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

* refactor: simplify SDK types by using @anthropic-ai/claude-agent-sdk types directly

- Remove duplicate SdkRunOptions and McpStdioServerConfig types
- Use SDK's Options and McpStdioServerConfig types directly
- Return { sdkOptions, showFullOutput, hasJsonSchema } from parseSdkOptions
- Remove unnecessary convertMcpServers function
- Net reduction of ~70 lines

🤖 Generated with [Claude Code](https://claude.com/claude-code)

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

* refactor: use extraArgs for claudeArgs pass-through to CLI

Simplify option parsing by converting claudeArgs to extraArgs record
and letting the SDK/CLI handle --mcp-config, --json-schema, etc.

- Remove extractJsonSchema and parseMcpConfigs functions
- Add parseClaudeArgsToExtraArgs for simple flag parsing
- CLI handles complex args like --mcp-config directly

🤖 Generated with [Claude Code](https://claude.com/claude-code)

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

* ci

* refactor: remove hardcoded permission bypass flags

The SDK path should match CLI path behavior - permissions are handled
by the CLI itself, not hardcoded in the action.

🤖 Generated with [Claude Code](https://claude.com/claude-code)

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

* chore: add logging for SDK vs CLI path selection

---------

Co-authored-by: Claude <noreply@anthropic.com>

.github/workflows/test-base-action.yml

@@ -118,3 +118,61 @@ jobs:
             echo "❌ Execution log file not found"
             exit 1
           fi
+
+  test-agent-sdk:
+    runs-on: ubuntu-latest
+    steps:
+      - uses: actions/checkout@11bd71901bbe5b1630ceea73d27597364c9af683 # v4
+
+      - name: Test with Agent SDK
+        id: sdk-test
+        uses: ./base-action
+        env:
+          USE_AGENT_SDK: "true"
+        with:
+          prompt: ${{ github.event.inputs.test_prompt || 'List the files in the current directory starting with "package"' }}
+          anthropic_api_key: ${{ secrets.ANTHROPIC_API_KEY }}
+          allowed_tools: "LS,Read"
+
+      - name: Verify SDK output
+        run: |
+          OUTPUT_FILE="${{ steps.sdk-test.outputs.execution_file }}"
+          CONCLUSION="${{ steps.sdk-test.outputs.conclusion }}"
+
+          echo "Conclusion: $CONCLUSION"
+          echo "Output file: $OUTPUT_FILE"
+
+          if [ "$CONCLUSION" = "success" ]; then
+            echo "✅ Action completed successfully with Agent SDK"
+          else
+            echo "❌ Action failed with Agent SDK"
+            exit 1
+          fi
+
+          if [ -f "$OUTPUT_FILE" ]; then
+            if [ -s "$OUTPUT_FILE" ]; then
+              echo "✅ Execution log file created successfully with content"
+              echo "Validating JSON format:"
+              if jq . "$OUTPUT_FILE" > /dev/null 2>&1; then
+                echo "✅ Output is valid JSON"
+                # Verify SDK output contains total_cost_usd (SDK field name)
+                if jq -e '.[] | select(.type == "result") | .total_cost_usd' "$OUTPUT_FILE" > /dev/null 2>&1; then
+                  echo "✅ SDK output contains total_cost_usd field"
+                else
+                  echo "❌ SDK output missing total_cost_usd field"
+                  exit 1
+                fi
+                echo "Content preview:"
+                head -c 500 "$OUTPUT_FILE"
+              else
+                echo "❌ Output is not valid JSON"
+                exit 1
+              fi
+            else
+              echo "❌ Execution log file is empty"
+              exit 1
+            fi
+          else
+            echo "❌ Execution log file not found"
+            exit 1
+          fi