Bark primarily focuses on monitoring the account it is installed on, which in this case would be the Discord account logged in on your phone where the Bark app is active. If you log into additional Discord accounts on different devices, Bark will not automatically know about those accounts or be able to monitor them unless the Bark app is specifically installed and configured to monitor those accounts as well.
In summary, Bark will only monitor the Discord account linked with the Bark app on your phone. Other accounts logged into on your desktop or in different locations won't be monitored unless those specific accounts are also set up under Bark's monitoring protocols. Always check Bark's official guidelines or customer support for the most accurate and up-to-date information regarding their services and features.