How to connect ESP8266 to WS8212b ribbon using existing power supply?

malymakar wrote:

Is there a chance in a relatively simple way to splice this tape and power supply to the ESP8266?

Clear. Just why 4 cables from the tape? Do you have a version with two data lines?
The connection is simple, you install the WLED, 5V is connected under the ESP and under the tapes, tape communication to the selected ESP pin and that's it.

Ah, I see. You have a double ground.
On the ESP install the WLED. From what I remember there was a website that only worked on Chrome, the browser had access to the serial ports of the computer and was able to install WLED directly on the ESP. I'll look for it, maybe I'll find it.
Power supply and "thicker" ground you connect to the power supply. To the ESP you connect (in addition to the power supply) the "thinner" ground from the tape, and the signal wire. You turn on the ESP, log in to WLED and in the configuration panel you set the tape type, its parameters including length in leds, and on which pin it should issue the data signal for the tape. It is to this pin that you connect the tape signal. A trivial matter, especially when you have everything specified in the application.

malymakar wrote:

and the power supply somehow has to be added separately?

To the ESP? Of course. It can be the same 5V as for the LEDs.