I want to have one ESP32 who sends data via BLE to the other three ESP32's.
At the end, the main ESP32 will get information if a certain button is pressed (the buttons are connected to the ESP32 through jumper wires) and send this information via bluetooth to the other three ESP32's (they would light up a specific LED).
I just want to ask, would such a project be possible?
And is BLE recommandable for it?
Possible, yes, but not via BT. That's a communication between two paired units. What would it look like if Your neighbour hooks into Your phone BT, or changes Your TV?
RF, radio...
As I'm not radio active I suggest google on Ardiino + RF. Threre are several thinkable alternatives having different ranges, prices, data rates etc.
Hopefully some radio guy steps in giving more advice.