Device to loopback mic to headphones
The headset speaker impedance is 32ohms each and the microphone impedance is 2200 ohms.
Most of your answer is in that statement. The mic and speakers will act as a potential divider of \$ \frac {32}{2200+32} \$ giving about 1.5% of the mic output (which was already a small signal) to the 32 Ω speakers. It won't work.
What you are seaking is called "sidetone" and was used in ordinary old-fashioned telephones so you might gain some insight by searching for telephone sidetone.
Obviously you cannot feed the mic signal back with the available settings in "the device", so you need a mixer - one which accepts your mic signal as one mono input and the headphone signals as one stereo input. The mixer should be able to supply your mic with the common 1...3VDC, if the mic is of the usual electret type.
The stereo input should be able to handle headphone signal level, which is pretty much more than normal audio device line signals.
The mixer should be able to produce the needed output power for your headphones and split the mic signal to where it's actually used.
I bet someone has already invented this device and it's for sale somewhere. Unfortunately I do not know, where
If I needed it, I would build it - one battery, one dual audio amp IC, one potentiometer, few caps and few resistors and proper case+connectors, maybe also a battery switch if it cannot be a part of a connector.
ADD due questioner's new attempt:
Split = branch a wire as you have done, only be sure that the possible mic supply voltage DC from "the device" doesn't get into your own circuit. 1uF cap in your circuit does the separation, no need to add parts. Remove 10kOhm resistor between the mic wire and your own battery, the mic gets its DC from "the device". Find how to change your amp to be a summing amp which gets another signal from the headphone output of "the device". Let your headphones get signal only from your amp. Now you have very inefficient passive mixer, it's well possible you get too low volume to the headphones.
You need 2 amps if you want listen as stereo. If you accept mono listening, one amp is enough.
Your amp IC of choice NJM2113 is designed to make a bridged speaker amp. That cannot be utilized because from your own schematic I can see you seem to have only single ended (=L,R,GND) headphone wiring. But the output power can still be enough because you get over 1Vpp.
NJM2113 has low maximum voltage gain. I inserted a mic preamp. It's here:
Hopefully NJM2113 doesn't generate too much noise and stays stable with low current loads and the other bridge output as unloaded. How much gain you really need, that can only be guessed. Increasing R1 increase gain, decreasing R1 makes gain smaller. C1 should be reduced if there's still too much bass umble. If you want more bass, increase C1. I have assumed your mic system (=headset + "the device" together) look outwards as 2kOhm signal source and you get 5mV signal.
The mixer (only one amp is drawn, the +3V supply is common to all amps):
The mixer outputs headphone speaker voltage without amplification. Mic preamp output voltage is amplified to 2500%. At the output you see the common zobel circuit to ensure some resistive loading. Inductive headphones alone would easily make the circuit unstable. There's 100uF coupling caps for the headphones. Anything less will kill the bass. The battery has 100uF bypassing. I hope it's enough to prevent signal feedback via battery lines.
Hopefully you can make the wiring so that output's current doesn't go through the GND wires which feed input signal to the mic preamp IC. If not, do not expect stable function.
EDIT: This circuit has a trivial error. The preamp input is in current mode, it pulls the mic output signal to knees and the original audio device gets nothing altough in the headphones the signal is loud. It's fixed in the discussion. The idea is to change the preamp circuit to non-inverting which has high Z input. The questioner drew the fixed image for his Edit 5: https://i.stack.imgur.com/DZl1x.png