feat: cleanup chat panel (#14259)

#### PR Dependency Tree


* **PR #14258**
  * **PR #14259** 👈

This tree was auto-generated by
[Charcoal](https://github.com/danerwilliams/charcoal)

<!-- This is an auto-generated comment: release notes by coderabbit.ai
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## Summary by CodeRabbit

* **Refactor**
* Split AI initialization into separate editor, app, and shared
registries; removed legacy chat-panel and replaced it with a
component-based editor chat, updating wiring and public exports.
* Propagated server/subscription/model services into chat/playground
components and improved session lifecycle and UI composition.

* **Tests**
* Added tests for AI effect registration and chat session resolution;
extended DOM/test utilities and assertions.

* **Chores**
  * Added happy-dom for runtime and test environments.

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packages/frontend/core/package.json

@@ -109,6 +109,7 @@
     "@types/semver": "^7",
     "@vanilla-extract/css": "^1.17.0",
     "fake-indexeddb": "^6.0.0",
+    "happy-dom": "^20.3.0",
     "lodash-es": "^4.17.21",
     "vitest": "^3.2.4"
   }