feat(chat): implement AI SDK integration with custom streaming response handling (#11901)

### Changes 🏗️

- Added AI SDK integration for chat streaming with proper message
handling
- Implemented custom to_sse method in StreamToolOutputAvailable to
exclude non-spec fields
- Modified stream_chat_completion to reuse message IDs for tool call
continuations
- Created new Copilot 2.0 UI with AI SDK React components
- Added streamdown and related packages for markdown rendering
- Built reusable conversation and message components for the chat
interface
- Added support for tool output display in the chat UI

### Checklist 📋

#### For code changes:
- [x] I have clearly listed my changes in the PR description
- [x] I have made a test plan
- [x] I have tested my changes according to the test plan:
  - [x] Start a new chat session and verify streaming works correctly
  - [x] Test tool calls and verify they display properly in the UI
  - [x] Verify message continuations don't create duplicate messages
  - [x] Test markdown rendering with code blocks and other formatting
  - [x] Verify the UI is responsive and scrolls correctly

#### For configuration changes:

- [x] `.env.default` is updated or already compatible with my changes
- [x] `docker-compose.yml` is updated or already compatible with my
changes
- [x] I have included a list of my configuration changes in the PR
description (under **Changes**)

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Co-authored-by: Lluis Agusti <hi@llu.lu>
Co-authored-by: Ubbe <hi@ubbe.dev>