If I understand correctly modern microphones integrated with headphones with 4-contact 3.5mm jacks for use with cell phones are condenser microphones, and usually contain a small, integrated amplifier - consisting of at least one FET and a few passives for bias isolation.
These are very low current, but require a small DC bias available from the microphone input to operate, and usually a resistor divider there requires and draws at least a small current.
Question: Is there a standard, or generally and widely accepted minimum current that a designer can expect any modern phone to make available at the 3.5mm 4-contact plug - or voltage plus maximum internal series resistance (within the phone)? I'm guessing it's going to be somewhere in the ballpark of 1 to 100 micro-amperes and between 1 and 2 volts, but I don't actually know this for sure.
Here is just a random example, the TPA6166A2 3.5-mm Jack Detect and Headset Interface IC was the first I found in a search, and it seems to be rated to supply a maximum of 1.2 mA when it detects a need for it and the internal bias resister is set to bypass. However it is no evidence by itself of a minimum standard.
There are plenty of examples, and other questions within this stackexchange, but so far I haven't found the actual published, or industry accepted minimum current, or minimum voltage plus maximum internal(phone) series resistance.
Hypothetical use example: This is not what I'm doing but it's a good working example for the question. "pico-LEDs" - small surface mount LEDs attain useable brightness at only a few milliamperes. A power harvesting-like circuit could collect enough charge from say 50 microamperes over one minute to "blink" the LED for 100 milliseconds.
above: screenshot from an example picoLED-eco surface mount LED.
Comments on personal experience are welcome, but for an answer I need a link to a real, relatively reliable specification from which design something with the reasonable expectation that it should work with any modern cellphone with the 3.5mm 4-contact plug and draw a small but useful amount of power from it (microwatts).