First, recognize that each fan you have has TWO cables from it. For each, ONE of them has 4 holes and two ridges down one side, and these are for the fan MOTOR only. The OTHER connector is wider with 3 holes (looks like it had 4 but one is blocked off) and this is for the LIGHTS only.
The NZXT website is not clear on this detail, but it seems to indicate that the fan LIGHTING cables on their units are non-standard locking connectors, but that may not be so. They MAY all connect to one NZXT lighting HUB. The case manual clearly shows that you must plug ONE cable and connector for the lights into a mobo standard 3-pin ARGB header, so presumably that will get those three fans lit up.
The manual for the MSI cooler system you have indicates that it needs to have a place to plug in the lights from FOUR units - the pump and three rad fans - but does not show how this is done. Unless it includes a LIGHTING Splitter cable to connect all four to a single mobo ARGB header, you will need such a device like this
https://www.amazon.com/Cooler-Master-Addressable-Universal-Radiators/dp/B083X1W5G4/ref=sr_1_8?crid=3T7ER35O42Q87&keywords=argb+splitter+3+pin&qid=1704218535&sprefix=ARGB+Splitteer,aps,106&sr=8-8
NOTE that this one is the 3-pin style for ARGB lighting, and it has five outputs. That could cover all four items from the cooler system plus one output to the group of case fans.
However, IF the MSI system does come with a lighting Splitter to connect all to a single header, AND your mobo has TWO ARGB headers (the second for the case fan light group), that would be all you need. You have not told us exactly what mobo you have - maker and model.