Replace Langbase with runLLM widget integration

- Removed @langbase/components and langbase dependencies
- Removed custom chat components and API routes
- Added runLLM widget via Next.js Script component in layout.tsx
- Configured runLLM with Sourcegraph brand styling
- Added AGENTS.md with integration documentation
- Assistant ID placeholder needs to be updated with actual ID

Co-authored-by: Amp <amp@ampcode.com>
Amp-Thread-ID: https://ampcode.com/threads/T-92230f6d-ca98-498f-8898-bffc173575ef

Author: mibali

AGENTS.md

@@ -0,0 +1,54 @@
+# Sourcegraph Docs - Agent Instructions
+
+## Build Commands
+
+- **Type Check**: `npx tsc --noEmit`
+- **Build**: `npm run build` 
+- **Dev**: `npm run dev`
+- **Lint**: `npm run lint`
+
+## AI Chat Integration
+
+This site uses **runLLM** for the AI chat widget. The integration is implemented via:
+
+- **Location**: `src/app/layout.tsx`
+- **Widget**: runLLM script loaded via Next.js `<Script>` component
+- **Configuration**: 
+  - Position: BOTTOM_RIGHT
+  - Theme color: #FF5543 (Sourcegraph brand color)
+  - Button text: "Ask AI"
+  - Keyboard shortcut: Mod+j
+
+### runLLM Configuration
+
+To update the runLLM assistant ID or other settings, modify the Script component in `src/app/layout.tsx`:
+
+```tsx
+<Script
+  id="runllm-widget-script"
+  type="module"
+  src="https://widget.runllm.com"
+  crossOrigin=""
+  runllm-keyboard-shortcut="Mod+j"
+  runllm-name="Sourcegraph AI Assistant"
+  runllm-position="BOTTOM_RIGHT"
+  runllm-assistant-id="YOUR_ASSISTANT_ID"  // Update this
+  runllm-theme-color="#FF5543"
+  runllm-floating-button-text="Ask AI"
+  async
+/>
+```
+
+### Previous Integration
+
+Previously used **Langbase** with custom React components. This has been completely removed:
+- Removed `@langbase/components` and `langbase` packages
+- Removed custom chat components (`src/app/chat.tsx`, `src/components/ChatBot/`)
+- Removed API routes (`src/app/api/chat/`)
+- Removed memory creation scripts
+
+## Important Notes
+
+- **Assistant ID**: The `runllm-assistant-id` is currently set to "YOUR_ASSISTANT_ID" and needs to be updated with the actual Sourcegraph runLLM assistant ID
+- **Deployment**: After updating the assistant ID, add the deployment URL to the runLLM dashboard
+- **Styling**: The widget inherits the site's theme and uses the Sourcegraph brand color (#FF5543)