The pump and rad fans of that AIO cooler system are of the 4-pin type, and they can NOT be connected to a mobo 3-pin ARGB header. They wont work. You have five choices.
1. IF your mobo ALSO has a 4-pin plain RGB header (we can't tell because you have not told us what mobo you have), you can plug them into that. Then those items will light up and you can control them, but they will never sync with the ARGB case fans.
2. Again, IF your mobo has a 4-pin plain RGB header (above) AND you REALLY want to sync all the lights, there is one way. BUT what it does is force the ARGB case fans to behave like the much simpler plain RGB fans, so you lose all the fancy multi-colour displays that ARGB devices can do. So, if you really want to do it this way, get an converter like this
https://www.amazon.com/EZDIY-FAB-Converter-Transfer-Splitter-Motherboard/dp/B082KJH2T3/ref=sr_1_1?crid=37Z0LUH9VZXDJ&dchild=1&keywords=ezdiy-fab+rgb+converter,+12v+rgb+to+5v+argb&qid=1607909254&sprefix=ezdiy-fab+converter,aps,190&sr=8-1
plus a plain RGB Splitter like this 2-pack
https://www.amazon.com/Splitter-Con...1&keywords=rgb+splitter&qid=1607909380&sr=8-6
The Splitter has female (with holes) connectors on each end, and comes with little gender-changer adapters so you can convert four output ends to males. That will give you four plain RGB outputs from one mobo header, so you can connect the cooler system pump and fans to this, plus use the fourth output to feed the Converter. The Converter is a box that can generate displays all by itself (which you don't want) BUT also can be set (by holding down one of its buttons) to let the signals fed from the mobo header take control. The box has a two-headed cable: one plugs into a SATA power connector from the PSU for power, and the other plugs into a male plain RGB output to get the control signal from the mobo. The box has one 3-pin ARGB output port and comes with a three-from-one Splitter so you can connect all three case ARGB fans to it instead of to the mobo ARGB header. With this combination plus a mobo plain RGB header, you can get all your lights to sync together as plain RGB, but you will NOT get the fans' ARGB type displays.
3. If your mobo has no plain RGB (4-pin) mobo header, you could buy a third-party plain RGB controller box and plug your AIO system lights into that to light and control them. They will not be controlled by your mobo, and they will not sync with the case fans.
4. Replace the rad fans of your AIO system with new rad fans of the 3-pin ARGB lighting type. Get a 3-pin ARGB Splitter so you can connect them to the same mobo header that feeds your case fans. Forget about the lights in the pump, and just use the fan lights.
5. Forget about all the AIO system lights. Just use the case fan lights you have already.