chore: migrate from deprecated @anthropic-ai/claude-code to @anthropic-ai/claude-agent-sdk

Anthropic rebranded the SDK in 2025 from "Claude Code SDK" to "Claude Agent SDK". Updated all references across package.json, Dockerfile, and documentation to use the current @anthropic-ai/claude-agent-sdk package.

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

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

package-lock.json

@@ -9,7 +9,6 @@
       "version": "1.0.0",
       "dependencies": {
         "@anthropic-ai/claude-agent-sdk": "^0.1.0",
-        "@anthropic-ai/claude-code": "^1.0.96",
         "ajv": "^8.12.0",
         "ajv-formats": "^2.1.1",
         "boxen": "^8.0.1",
@@ -44,26 +43,6 @@
         "zod": "^3.24.1"
       }
     },
-    "node_modules/@anthropic-ai/claude-code": {
-      "version": "1.0.96",
-      "resolved": "https://registry.npmjs.org/@anthropic-ai/claude-code/-/claude-code-1.0.96.tgz",
-      "integrity": "sha512-xnxhYzuh6PYlMcw56REMQiGMW20WaLLOvG8L8TObq70zhNKs3dro7nhYwHRe1c2ubTr20oIJK0aSkyD2BpO8nA==",
-      "license": "SEE LICENSE IN README.md",
-      "bin": {
-        "claude": "cli.js"
-      },
-      "engines": {
-        "node": ">=18.0.0"
-      },
-      "optionalDependencies": {
-        "@img/sharp-darwin-arm64": "^0.33.5",
-        "@img/sharp-darwin-x64": "^0.33.5",
-        "@img/sharp-linux-arm": "^0.33.5",
-        "@img/sharp-linux-arm64": "^0.33.5",
-        "@img/sharp-linux-x64": "^0.33.5",
-        "@img/sharp-win32-x64": "^0.33.5"
-      }
-    },
     "node_modules/@img/sharp-darwin-arm64": {
       "version": "0.33.5",
       "resolved": "https://registry.npmjs.org/@img/sharp-darwin-arm64/-/sharp-darwin-arm64-0.33.5.tgz",