I don’t know if this has been talked about in the past, but I’m new to the iPhone, so I’m not sure how this works. When I toggle the WiFi or Bluetooth off on the control Center, it shows a message that says: turning off Bluetooth WiFi communications until tomorrow. Does this mean that it’s just not turning off at all? Turning it off from the settings seems to help, but doing it from control Center simply does nothing.
Turning it off from the control center should give you the message you mentioned, but turning it back on writes a message to the iphone Control Center Screen. Maybe when you tried it in Control Center you were turning it back on. I'd try it again from Control Center and press the bluetooth button twice to make sure you get it off and on. After pressing be sure to check the top of the Control Center screen.