From a number to volts

A count is a fraction

An analog pin does not report volts. It reports how far up its range the voltage is, as a whole number: 0 at the bottom, the largest count at the top. On an Uno that range is 0 to 1023 against its 5 V supply. On a Pico running arduino-pico it is 0 to 1023 against 3.3 V, unless the sketch asks for 12 bits.

So a count is a fraction of the board's reference voltage:

SIG   = count × VREF / ADC_MAX
input = SIG × 5

An Uno reading 368 has SIG at 368 × 5.0 / 1023, which is 1.80 V, and the input at five times that, 8.99 V.

One step of the input

The count moves in whole steps, so the input does too. On an Uno one count is 5 V / 1023, about 4.9 mV on SIG, and five times that on the terminal: about 24 mV. A 9 V battery reads to the nearest fortieth of a volt, which is finer than its own voltage stays still.

On a Pico at the default 10 bits, one count is about 16 mV of input. Call analogReadResolution(12) and change ADC_MAX to 4095, and it is about 4 mV.

The ESP32 does its own conversion

The ESP32 and ESP32-S3 have a 12-bit ADC, 0 to 4095, but a count there is not a clean fraction of 3.3 V. With the Arduino core's default setting the ADC reads only to about 3.1 V, and its response bends near both ends. Dividing a raw count by 4095 and multiplying by 3.3 gives a number that is off by different amounts at different voltages.

Each chip carries calibration data for its own ADC. analogReadMilliVolts applies it and returns SIG in millivolts, so the sketch divides by 1000 and multiplies by five. MicroPython's read_uv does the same in microvolts. That is why the sketches treat the ESP32s separately: not a different formula, but a better first step.