This thread already discusses it: Export Audio/Group Channel inconsistency - #6 by Sonik
Basically, Audio Mixdown will NOT print fx routing, while Render in place does. So a workaround when you want to print a group (that cannot be rendered in place) is to temporary route the fx channels to the group you’re mixing down. But then if you do that, those fx channels will include signal from other tracks in the project, that you don’t want to print. And soloing the group might interfere with sidechain info.
The only real “solution” is to live export, right?
EDIT: Live / Real-time export won’t do the trick as well…