With the right software, ESP32 can be incredibly low power. Like "months on 3xAA batteries" for watching a pin with the ultra low power subsystem and then occasionally waking up and making a HTTPS call over WiFi.
Bluetooth is lower energy than WiFi, but in your scenario the energy used for the radio is quite low anyway.
I never did a formal study to see how much of that power use was standby vs. power-on usage, how much of the standby usage was the ESP32 vs. the board/voltage regulators/pulldowns, how much of the power on usage was radio vs. e.g. all the crypto (we're doing asymmetric crypto for the TLS handshakes on batteries here, that isn't going to be cheap!) etc.
I just slapped it together and found it good enough to not care further.
You can use a different resistor according to the power draw and how sensitive your volt meter is.
You'll probably need to power it up with the resistor shorted, and only remove the short once it's in sleep mode, to measure the current.