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>

bun.lock

@@ -6,6 +6,7 @@
       "dependencies": {
         "@actions/core": "^1.10.1",
         "@actions/github": "^6.0.1",
+        "@anthropic-ai/claude-agent-sdk": "^0.1.52",
         "@modelcontextprotocol/sdk": "^1.11.0",
         "@octokit/graphql": "^8.2.2",
         "@octokit/rest": "^21.1.1",
@@ -35,8 +36,40 @@
 
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