So I could you this controller with a AC to DC power supply? How would I wire the rings up to that controller, since each ring has it's own cable?

https://www.amazon.com/BTF-LIGHTING-C02Z-Controller-Compatible-Dual-Mode/dp/B0B2J2NVZB/ref=mp_s_a_1_2_sspa?crid=32DW9IBQGKOTP&keywords=cct+led+controller&qid=1675557607&sprefix=cct+led+co%2Caps%2C211&sr=8-2-spons&psc=1&spLa=ZW5jcnlwdGVkUXVhbGlmaWVyPUEyNUs4RDNNWUNRMDJZJmVuY3J5cHRlZElkPUEwNzM2MDc0MzU0SFhXVU9SSlhTOCZlbmNyeXB0ZWRBZElkPUEwOTU1NzY0MlJYN0lON0paSFZJSCZ3aWRnZXROYW1lPXNwX3Bob25lX3NlYXJjaF9hdGYmYWN0aW9uPWNsaWNrUmVkaXJlY3QmZG9Ob3RMb2dDbGljaz10cnVl

You need a CCT controller for the white strip.

Zigbee https://www.amazon.com/BTF-LIGHTING-C02Z-Controller-Compatible-Dual-Mode/dp/B0B2J2NVZB/

WiFi: https://www.amazon.com/BTF-LIGHTING-FUT035W-Temperature-2700K-6500K-Controller/dp/B096VN5NS1

Note these controllers are like half the price on AliExpress if you're willing to wait 2-3 weeks.