feat: reorganize tabs + add Last Prompt CC/Fallback toggle

- Split Status tab: moved DM management to new dedicated 📱 DM Management tab
- Added Last Prompt source toggle (Cheshire Cat / Bot Fallback) with
  localStorage persistence, CC as default
- Backend: added LAST_CAT_INTERACTION global, /prompt/cat API endpoint
- Bot tracks Cat interactions (prompt, response, user, mood, timestamp)
- Auto-load data on tab switch (Status loads prompt, DM tab loads users)

bot/api.py

@@ -201,6 +201,14 @@ def get_logs():
 def get_last_prompt():
     return {"prompt": globals.LAST_FULL_PROMPT or "No prompt has been issued yet."}
 
+@app.get("/prompt/cat")
+def get_last_cat_prompt():
+    """Get the last Cheshire Cat interaction (prompt + response) for Web UI."""
+    interaction = globals.LAST_CAT_INTERACTION
+    if not interaction.get("prompt"):
+        return {"prompt": "No Cheshire Cat interaction has occurred yet.", "response": "", "user": "", "mood": "", "timestamp": ""}
+    return interaction
+
 @app.get("/mood")
 def get_current_mood():
     return {"mood": globals.DM_MOOD, "description": globals.DM_MOOD_DESCRIPTION}