Have at it, lore nerds! 
https://screenrant.com/hitman-freelancer-jonas-breum-jensen-torbjorn-vinther-christensen/
When does Freelancer take place on the Hitman game timeline, if it does at all?
JBJ: Freelancer exists in a separate parallel timeline. On the one hand the narrative of being a freelancer and operating solo with Diana, but without belonging to a bigger organization like ICA, fits with where the story of where Hitman 3 ends. But on the other hand the actual on-mission gameplay in Freelancer takes place on the same time as the main missions, in most cases, so that gives a narrative disconnect to make the post-Hitman 3 idea work fully.
We decided that it was preferable to keep most of the main-mission content in the Freelancer versions of the maps, rather than flushing that layer, because it gives more gameplay opportunities to the sandboxes than the vanilla versions would do. But we also decided to leave a bit of ambiguity so that players who like to pretend that the gameplay takes place after Hitman 3 can do that, without too much distraction from the established canon.
TVC: Early on in development we had to choose between reworking a few locations to fit the timeline to post Hitman 3 or use almost all locations in the trilogy in Freelancer. In our minds the choice was easy, as we wanted to get the biggest possible playground for the game mode.