I think I've run into a bug.
It installed just fine, I could purchase the suit and put it on.
I have since then changed my outfit and now when I want to put it back on, be it through the gateway wardrobe or any clothing shop, I bug out.
In the Gateway, I get the classic freeze, background and noise etc continue, but no menu pops up and only taskmanager closing works.
In the shops the HUD vanishes and I'm just looking at my character, everything continues, no actual freezing happens, I just can't do anything anymore except for Taskmanager closing.
I've rebooted the game five times now, tried a different shop/gateway each time, same result.
Scratch this, turns out I forgot I had a customisation mod that's interfering with the Cruise Control Mod I installed yesterday, sounds like this one is right up that alley.