My five cents: do you have a heat sink on the 7805?
(how large: for 4 W at least?)
Drawing 300 mA (for MCU) with a voltage drop from 12V down to 5V - gives you 7V *0.3A = 2.1W burned power. It is a lot.
Without a proper heat sink - the 7805 will enter immediately the thermal protection (and shuts down).
BTW:
You try to power audio amplifiers from the 3V3 rail, provided by your MCU module?
Are you sure they can provide so much current? (they had to power the MCU - nothing else, but now also so much current for the audio power amps?).
Just take your 7805, powered by 12V, put just a 10 Ohm load resistor on it (on 5V out, instead of MCU), but as a 3.5 .. 5W type (!!) and see if voltage remains stable.
It tries to draw 0.5A from 7805. I assume - 7805 gets so hot ... (and shuts down immediately).
I have changed the capacitors for the regulator so it is 470uF on the input and 1000uF on the output as well as 0.1uF ceramic.
I have also tried disconnecting everything and just tried powering the board, but it is not drawing enough current. I am starting to think it might be a faulty regulator but it is weird that it still regulates the voltage correctly.
I have also tried with a 9V power supply, but the same problem still persists.
Are the smoothing/crossover capacitors the ones connected from the amp to the speaker, because if so they are not connected yet but they are going to 2.2uF.
Please show us a diagram of it in your circuit.
Please include pin numbers and names, especially around the ESP32.
To what pin on the ESP32 do you have the 5V connected?