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RGB isn't my thing, but it looks like you've got a couple of choices. You can get cases that have controllable in-built lighting, some for not much money either
https://www.overclockers.co.uk/kolink-void-rgb-midi-tower-case-black-window-ca-04l-kk.htmlOr you could get whatever case you like and put in an RGB controller, some plug into a USB socket on the mobo and let you install software to control them. Some just use a Sata connection for power then have a little remote control. You can get complete systems or make your own
https://www.overclockers.co.uk/corsair-lighting-node-pro-rgb-lighting-controller-with-individually-addressable-rgb-led-strips-cm-000-cs.htmlI think you're out of luck trying to sync it to the accessories unless you move to Corsair, their Icue software looks like it'll do the job.
https://www.corsair.com/uk/en/icueOtherwise I imagine even using two different pieces of software to control the RGB in the case and the accessories it should be possible to make them match, like if you use the 'breath' fade you can usually control which colours and how long on each.
Only Steelseries can use PrismSync cos it's their own software. What's the case? You can get rbg controllers that you plug the fans in to them to the motherboard which may be an easier solution