Here's some background information that might be useful to understand what's going on.
The bare physics answer to “why is this happening” is: two wires running close together form an unintended capacitor. This capacitive coupling allows the signal in the headphone wires to cross over to the microphone wire. The longer the cable, the larger the capacitance, and therefore the stronger the effect.
The coupling effect can be reduced by careful design of the cable, such as placing separate shields around the microphone wire and around the headphone wires. I do not know if any commercially available TRRS extensions have this design.
However, you could assemble such a cable out of parts by using a pair of quality TRS extension cables (each of which has its own shield), then using TRRS-to-2×TRS adapters at both ends. This might solve your problem at the cost of having lots of bulky inline plugs.
One of my headsets includes a switch for muting the mic. When I move the switch into the mute position, the stereo signal leaks even more loudly into the mic signal!
The switch probably operates by disconnecting the microphone from the cable. This means the microphone signal wire is “floating”, not connected to and not driven by any intended source, and therefore nothing is competing with the capacitive coupling. It's the same idea as if you attached an unshielded wire to a microphone input, or touched the signal contact on a plug: you'd suddenly hear a lot of hum and other EMI. But in this case, instead of general fields in the air, you're picking up specifically the adjacent wire.
If I split the TRRS cable into two separate cables for microphone and headphones, and then split the TRS microphone jack into separate cables for the ring and sleeve but leave the sleeve disconnected, this causes the leakage to be incredibly loud.
Same idea as the switch — any time you have a wire that doesn't make a complete circuit it will mostly pick up interference. (If the wire is shielded, then the shield also picks up the same interference and the net effect is zero — or, looking at it from another angle, the ground connection of the shield drives the voltage on it, and therefore the local electric field, to zero from the perspective of the attached equipment, so the inner wire sees that zero instead of interference.)
(I don't understand why the mic uses a TRS jack if it's an unbalanced mono signal. Is the sleeve used for power?)
Yes, there is power, but it is on the ring contact if distinct at all. In practice, many PC-style microphones short together the tip and ring contacts (since electret microphone elements have only the 2 pins anyway and want bias power on them) and the later-developed TRRS connections enforce this since they only have one contact for mic audio and mic power. The sound card handles this by a capacitor on the audio line (to pass the audio and block the DC power) and a resistor on the power line (which prevents the power supply from suppressing the audio, and also provides current limiting in case the power is shorted out by e.g. connecting a TS passive microphone).
Because of this conflation, some PC microphone inputs may, for example, be stereo, with both the tip and ring providing power and (separate) microphone input.
(The name given to "PC-style" microphone powering is "plug-in power" — presumably originally some sound card manufacturer's marketing term.)
I just tested a headset on my iPhone 7 using an Apple lightning to 3.5mm adapter, and it doesn't have the leakage problem! But the standard 3.5mm TRRS headset port on my MacBook, iMac, and USB-C hubs all do have the problem.
That's interesting! That suggests that perhaps the impedance of the audio interface is relevant (because I can't think of anything else that would make such a difference).
If you're trying to pick up a weak signal, you can get the most power out of the signal source (here the microphone capsule) by impedance matching the receiver ("load") with the source. (However, audio connections are often impedance bridged instead, which simplifies design and makes it easier to achieve flat frequency response.)
The relevance here is that impedance matching causes the microphone capsule to put out the most signal power it can. Thus, it becomes relatively louder than the interference.
I don't know whether the Apple adapter actually does this. It would be potentially as simple as wiring a resistor of the right value across the input signal, causing current to flow, which the FET amplifier inside the electret capsule can supply better than the weak capacitive coupling can. (This description is a little weird to think about because the power source is actually from the adapter/computer and not the microphone, but the math works out the same as if the microphone itself were powered and driving the line.)