There's an internal pull-up on IO0 and pulldown on IO2, no need for external resistors.
https://www.esp32.com/viewtopic.php?t=5970

Can you share more of your code? Are you using an interrupt function triggered by the counter pulse?

What does ".counter_en = false " do?.

It's 1kHz, 40 divider, why do you expect 2000 counts? Is it run for 80 seconds?

The led is connected to TP4054 CHRG pin. With no battery connected, maybe it is doing the "charge complete / AC present" indicator of 20uA pull down. Are you seeing a bright flash or very dim? https://i.imgur.com/mwLLfeQ.png https://i.imgur.com/yWuAvCs.png Maybe your usb port is doing something like...

Read this post, it was published by espressif, you need to manually measure vref and then input it in your code as a calibration: https://www.esp32.com/viewtopic.php?f=19&t=2881&start=20#p16166 The analog_read function is not applying calibration or anything. So if you use analog_read, you must conv...

Yes as chegewara said the watchdog chip is simpler and less likely to fail and the esp32. So you have shifted the problem from the ESP 32 over to the watchdog chip, you shifted the problem from a more likely failure to a less likely failure and that is a success. You also can have a watchdog chip th...

Two point calibration will correct the offset and slope, thus you'll be more correct at both the low end and high end. Efuse vref can be single point or two point, obviously two point is a little better. Two Point values represent each of the ADCs’ readings at 150 mV and 850 mV. To obtain more accur...

avg_voltage = ((3.3/4095)*avg_dig_voltage)

I think you need the vref from efuse, about 1.1V. You said it read 1.46 when you measured 1.6, that would explain the difference.

Also I think it should be 4096, 2^12, not 4095

You could do a 555 timer that will pull the gate low after some short time like 50 ms. Then have your esp32 pulse to reset the 555 timer like every 40 ms. If your esp32 fails to reset the timer for any reason then the 555 will complete and pull the gate low. There are probably also watchdog chips th...

IO0 can float
EN must pull up

Look at the bottom of the module, the vias nearby do not have exposed copper. Follow the recommended footprint you should be fine. I guess if you were really concerned you could make them 1.35mm instead of 2mm (.85mm under module plus .5mm extending out from module). But generally the manufacturer's...