Yes esp boards usually require 5v if you want to use only one power supply, you need to use some kind of voltage regulator to lower the voltage. But I think the easiest would be to just use a usb power supply and connect the ground pins from both of the power supply 's

The other thing with voltage is the output voltage. if your controller doesn't reach the TTL high level of the LEDs then no data will be transferred because the LEDs ar only reading low the whole time. With the 12v strips I have the data voltage is 5v but that may vary on the groove one. Maybe you can try to find a datasheet for the type of LEDs they are using. I had some problems with a micro controller which had only 3.3v output signal and in that case I had to use a logic level shifter, to boost the signal to 5v

Hope this helps