refactor(bot): bot utilities into separate modules

Moved logging, signal handling, and uptime calculation logic from bot.py into dedicated utils modules for better organization and reusability. Updated imports and usage in bot.py and utils/__init__.py accordingly.

utils/time.py

@@ -0,0 +1,18 @@
+import time
+
+
+def get_uptime(start_time: float) -> str:
+    uptime_seconds = int(time.time() - start_time)
+    days = uptime_seconds // 86400
+    hours = (uptime_seconds % 86400) // 3600
+    minutes = (uptime_seconds % 3600) // 60
+    seconds = uptime_seconds % 60
+    
+    if days > 0:
+        return f"{days}d {hours}h {minutes}m {seconds}s"
+    elif hours > 0:
+        return f"{hours}h {minutes}m {seconds}s"
+    elif minutes > 0:
+        return f"{minutes}m {seconds}s"
+    else:
+        return f"{seconds}s"