To use Headwind MDM in the background mode, open the configuration details, and set the "Background mode" checkbox.
When this checkbox is set, Headwind MDM will not attempt to set itself as a default launcher, so the system launcher will be used as default. However Headwind MDM will work as a service, it will silently install required apps, monitor the device status, and perform other MDM tasks.
Note that this option couldn't be changed back easily in Android. You may need to re-enroll the device once you change it, apparently because of the Android OS bug.