Here is what I found today :
The 3.3v for the RF board comes from this 7533-1 component
From the datasheet, we can see that with a SOT-89 package, the typical output current is 100mA for 3.3V.
I measure Vin is around 6.2 Volts
I will try to put a buck DC/DC like this one in this board to power an esp32
The component whic uses the pwm signals is a BP2872
From the datasheet it’s Vcc should be 15v. Maybe another potential power supply for an esp…
=> it"s around 9,6 Volts but not enough power for an ESP through a buck 
https://datasheet4u.com/pdf-own/B/P/2/BP2872-BPS.pdf
This is your vital clue.
So I tested today a buck on the 6.2 Volts (which powers the 7533) and it is not enough for an ESP32-devki
I should try a less powerfull esp32
I’m giving up on hacking the power supply. It is a very low power supply so I think it is impossible to power an ESP32 in it unless using a dedicated AC/DC converter.
On the remote, with a piece I wire, I can control the lamp like in this example
I will try with an optocoupler
Another option could be to analyze signals coming out the “logic component” to the “RF component” to recreate them from an ESP32.
