feat: fix slash commands, add badge UI, multi-provider management

Slash commands:
- Fix skills not appearing (removed non-existent `enabled` filter)
- Add badge/capsule UI for prompt-type commands (/compact, /review, etc.)
- SDK-native commands sent directly; CLI-only commands expanded to prompts
- /clear now resets SDK session and clears database messages
- /cost shows actual aggregated token usage statistics
- Keyboard: Backspace/Escape to remove badge, arrow keys auto-scroll popover
- Add /memory command for editing CLAUDE.md

Multi-provider management:
- CRUD API for API providers with SQLite storage
- ProviderManager UI with quick presets (GLM, Kimi, MiniMax, etc.)
- Dynamic model labels based on active provider
- Environment variable injection with conflict resolution

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

src/app/api/chat/sessions/[id]/route.ts

@@ -1,5 +1,5 @@
 import { NextRequest } from 'next/server';
-import { deleteSession, getSession, updateSessionWorkingDirectory, updateSessionTitle, updateSessionMode } from '@/lib/db';
+import { deleteSession, getSession, updateSessionWorkingDirectory, updateSessionTitle, updateSessionMode, clearSessionMessages } from '@/lib/db';
 
 export async function GET(
   _request: NextRequest,
@@ -40,6 +40,9 @@ export async function PATCH(
     if (body.mode) {
       updateSessionMode(id, body.mode);
     }
+    if (body.clear_messages) {
+      clearSessionMessages(id);
+    }
 
     const updated = getSession(id);
     return Response.json({ session: updated });