Persist bot mode across restarts via database

Adds a BotSettings key-value table. The active mode is saved
when changed via /bcs-mode and restored on startup.

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

bot.py

@@ -104,6 +104,14 @@ class BCSBot(commands.Bot):
             loaded = self.drama_tracker.load_user_states(states)
             logger.info("Loaded %d user states from database.", loaded)
 
+            # Restore saved mode
+            saved_mode = await self.db.load_setting("current_mode")
+            if saved_mode:
+                modes = self.config.get("modes", {})
+                if saved_mode in modes and isinstance(modes.get(saved_mode), dict):
+                    self.current_mode = saved_mode
+                    logger.info("Restored saved mode: %s", saved_mode)
+
         await self.load_extension("cogs.sentiment")
         await self.load_extension("cogs.commands")
         await self.load_extension("cogs.chat")