The stripe drives very likely 5 or 6 LEDs as once, so every 5 centimeters will have the same color. This is how higher than 5 V are commonly achieved with that addressable light modules (I did not find a 12V or 24V yet where each LED is addressable individually).
You could have a look into my controller project which would be capable of driving this LEDs (LED power supply is completely independent of the controller as long as GNDs are connected. The controller can be run at 24V using the same power source): My PCB for ESP32 with 8 LED channels - #4 by micw. I’m not familar with the other available controllers but all should do as long as you can power the stripe directly.
According to the page I found, the stripe has 21 watts per meter. So 12m have ~250 Watts and a 300W PSU should do the job. An issue might be that the stripe will draw ~20 amperes. It is very unlikely that the stripe itself is able to carry that much power. That means that you either need to split the stripe into individual segments or that you need to feed power in every few meters (I’d say, ~every 2 or 3 meters).
Be also aware that you need AWG 14 wires (or > 2mm²) to transport >20 amps. I have a setup with similar power (but 12V). Here I have split up the stripes into 8 segments and I use WAGO connecting clamps to distrubute the power from the PSU to the individual stripes.
Example:
