I think it’s safe to assume that Freelancer operates on the same canon logic as ETs (and possibly Patient Zero, the Dmitri Fedorov mission, Holiday Hoarders, and the Special Assignments as well), where it does take place on the main timeline, but you have to suspend your disbelief and ignore the gameplay aspects to make the mode fit.
Obviously, you are not chasing these Syndicates on the exact same locations with the same time-of-day and the previous targets still there. It’s just represented that way because of the limitations of the game and what-not.
But the general events of 47 & Diana going Freelance and eliminating these new Syndicates can still perfectly fit into the post-H3 canon, though. It’s the same situation as the ICA Data Core where we learned the ET missions existed and were canon all along, but clearly 47 did not kill a dozen people at the same event where Viktor Novikov got tragically light-rigged, because it’s just completely incongruous to the main storyline.
So the existence of Syndicate Leaders, 47 and Diana as Freelancers, 47 getting the Safehouse and going after these Syndicates, all of these elements and events exist as they are in the canon timeline, just like the ETs themselves. It’s just the details of the locations where these missions take place that are different, again just like the ETs…