I log in to my Bambu account only when I know there’s a firmware update for the printer or the AMS. The rest of the time, it is logged out and the printer is connected in the LAN-only mode.
If you want to check the printer from the iPhone, there’s an iOS app called Bambu Companion. It’s in beta and uses Apple’s Test Flight for the install but it works quite well. Hopefully it will go general availability soon.
See this post: Bambu Companion for iPhone. No cloud needed - #2 by drakko