Official comment

The Mission Plan and Boundary part of Flight Sync was not introduce in Map Pilot until version 4.1.0 which Map Pilot Business has not been updated to yet.
https://support.dronesmadeeasy.com/hc/en-us/articles/206081996-Update-History
This Map Pilot Business update has taken a long time due to the iOS 13 update combined with all this sync stuff. There have been lots of fixes. 4.1.5 has been submitted which we hope will iron it all out.
In a pinch you could download the LITE version, pull your boundaries in and save your mission plans before sending them via .mme file to the older version.
I don't have a blue Sync button in the File Manager screen. I also do not have a "Boundary Sync" option in the settings menu.
Map Pilot 4.0.8, build 100120193