A few things to keep in mind when testing this:
I do perform an ADC read right before trying to connect to WiFi, since the ADC reading is affected by WiFi RF calibration.
But this is also right at boot, so that may be a current surge and thus the first reading upto the moment WiFi is connected may report a lower value than later samples.
This can be exactly what you need, as a discharged battery also shows increased internal resistance and thus the voltage may drop more at higher currents.
So just to keep in mind when testing this.
Another thing you should really look into is the quiescent current of the parts that are permanently connected to the battery, like the voltage regulator.
Most regulators, like the AMS1117 do have a terrible high quiescent current of 5 - 10 mA.
Meaning the voltage regulator alone does draw this current even when the ESP is in deep sleep.
Just one source of information on this subject:
https://randomnerdtutorials.com/esp8266 ... batteries/
You can get away with LDO regulators which only can handle 200 mA, but then you may need to include a capacitor very close to the ESP of 22uF - 100uF.
But these may cause a high current when they are empty and need to be charged. For this you may need to add a R/C delay to the EN pin to delay starting the ESP until these caps are fully charged.
This may require some tweaking.
If you use sendtohttp, you may want to check "SendToHTTP wait for ack" on Tools->Advanced page to make sure the command is finished by the rules.