Back when i used to use other software for windowmanagement, they used to have an option where i press a keybinding
and then the window below my mouse would act as if its Titlebar was being dragged.

This was helpfull for windows that woudnt have a Titlebar as some "StayOnTopWindowReplica" applications do.

Does DisplayFusion have this functionality? Or would i be able to mimic it somehow?

It sort of sounds like you're talking about the functionality of AltDrag? (the 3rd party program)

While the advanced scripting of DisplayFusion might make this possible, I'm unaware of it being built-in. Maybe someone can correct me.

With a normal window, you can do something like that by pressing Alt-Space, M, then a single arrow key of your choice. The window will be stuck to your cursor until you click. Doing this must send a specific WM message which could be emulated by a DisplayFusion script, but I don't know what specific message that would be.