That looks identical to the Gledopto controllers, I have a Gledopto branded RGBW version and it’s standards compliant and works with ZHA. Haven’t tried that specific brand or wled version, have done several projects with serial controller Rgb LED strips, but those were all DIY projects.
You can’t proceed with your plan because WLED only uses wifi. There are no zigbee controllers available at the moment which use WLED.
It might help if you answered the following questions
Did you buy these light strips already? If yes, then a model number & a link would be helpful.
Are you sure you need WLED? Do you need to actually control each individual LED within the strip? If yes, then zigbee controllers for individual LED control do not exist. The controller you linked to does not control individual LEDs - it will set the entire strip to whatever colour/white you choose*.
Is there a particular reason why you cannot use Wifi if you really need individual control?
*That controller is supported in Zigbee2Mqtt. Not sure about ZHA (the “default” zigbee in HomeAssistant), but at least you have options.