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>

base-action/bun.lock

@@ -5,6 +5,7 @@
       "name": "@anthropic-ai/claude-code-base-action",
       "dependencies": {
         "@actions/core": "^1.10.1",
+        "@anthropic-ai/claude-agent-sdk": "^0.1.52",
         "shell-quote": "^1.8.3",
       },
       "devDependencies": {
@@ -25,8 +26,40 @@
 
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+
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+
+    "@img/sharp-libvips-linux-x64": ["@img/sharp-libvips-linux-x64@1.0.4", "", { "os": "linux", "cpu": "x64" }, "sha512-MmWmQ3iPFZr0Iev+BAgVMb3ZyC4KeFc3jFxnNbEPas60e1cIfevbtuyf9nDGIzOaW9PdnDciJm+wFFaTlj5xYw=="],
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+
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+
+    "@img/sharp-linux-arm64": ["@img/sharp-linux-arm64@0.33.5", "", { "optionalDependencies": { "@img/sharp-libvips-linux-arm64": "1.0.4" }, "os": "linux", "cpu": "arm64" }, "sha512-JMVv+AMRyGOHtO1RFBiJy/MBsgz0x4AWrT6QoEVVTyh1E39TrCUpTRI7mx9VksGX4awWASxqCYLCV4wBZHAYxA=="],
+
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+
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+
+    "@img/sharp-linuxmusl-x64": ["@img/sharp-linuxmusl-x64@0.33.5", "", { "optionalDependencies": { "@img/sharp-libvips-linuxmusl-x64": "1.0.4" }, "os": "linux", "cpu": "x64" }, "sha512-WT+d/cgqKkkKySYmqoZ8y3pxx7lx9vVejxW/W4DOFMYVSkErR+w7mf2u8m/y4+xHe7yY9DAXQMWQhpnMuFfScw=="],
+
+    "@img/sharp-win32-x64": ["@img/sharp-win32-x64@0.33.5", "", { "os": "win32", "cpu": "x64" }, "sha512-MpY/o8/8kj+EcnxwvrP4aTJSWw/aZ7JIGR4aBeZkZw5B7/Jn+tY9/VNwtcoGmdT7GfggGIU4kygOMSbYnOrAbg=="],
+
     "@types/bun": ["@types/bun@1.2.19", "", { "dependencies": { "bun-types": "1.2.19" } }, "sha512-d9ZCmrH3CJ2uYKXQIUuZ/pUnTqIvLDS0SK7pFmbx8ma+ziH/FRMoAq5bYpRG7y+w1gl+HgyNZbtqgMq4W4e2Lg=="],
 
     "@types/node": ["@types/node@20.19.9", "", { "dependencies": { "undici-types": "~6.21.0" } }, "sha512-cuVNgarYWZqxRJDQHEB58GEONhOK79QVR/qYx4S7kcUObQvUwvFnYxJuuHUKm2aieN9X3yZB4LZsuYNU1Qphsw=="],
@@ -50,5 +83,7 @@
     "undici": ["undici@5.29.0", "", { "dependencies": { "@fastify/busboy": "^2.0.0" } }, "sha512-raqeBD6NQK4SkWhQzeYKd1KmIG6dllBOTt55Rmkt4HtI9mwdWtJljnrXjAFUBLTSN67HWrOIZ3EPF4kjUw80Bg=="],
 
     "undici-types": ["undici-types@6.21.0", "", {}, "sha512-iwDZqg0QAGrg9Rav5H4n0M64c3mkR59cJ6wQp+7C4nI0gsmExaedaYLNO44eT4AtBBwjbTiGPMlt2Md0T9H9JQ=="],
+
+    "zod": ["zod@3.25.76", "", {}, "sha512-gzUt/qt81nXsFGKIFcC3YnfEAx5NkunCfnDlvuBSSFS02bcXu4Lmea0AFIUwbLWxWPx3d9p8S5QoaujKcNQxcQ=="],
   }
 }