Mystery signal - FSK, BPSK?
After playing around in GNURadio, this waveform looks like 2 level ASK bursts (OOK bursts plus some residual carrier).

The carrier appears to be at 12.4 kHz.

At the 44.1 ksps sample rate, there appears to be about 7.6 samples/symbol or a symbol period of about 173.5 microseconds (assuming the symbols are not Manchester encoded).

See the top plot in the following image showing two filtered, rectified, and pulse filtered bursts.

 

Update to respond to comment

What I mean by 2-ASK with residual carrier is that, during a transmission, the original signal is probably something like:

$$(0.1 + 0.5q(t))\cos(2\pi 12400t)$$

where $q(t)$ is the train of unipolar message bit pulses.
With a square pulse matched filter in the receiver, one is going to get ISI, which you can see in the short (suspected) preamble of the bursts.

By the way, I have not checked the phase to see if the bursts are the real part of QPSK with a non-standard rotation (which would result in 4-QAM with constellation points only on the real axis), but that seems unlikely for a low parts count biometric headphone device.

The signal you provided was already low pass filtered with a corner at about 15-16kHz, indicating something was going to decimate this to a 32 ksps signal.

What I did in GNURadio is in the following flowgraph image:



I used the "Hilbert" block with a 201 tap Hilbert FIR filter to make the real signal analytic.  201 taps is obviously overkill, looking at the negative frequency side of the spectrum.

I then used a Blackman-Harris windowed high pass filter, with real taps, with a corner at 4 KHz, a transition width of 1 kHz, and an objective stop band attenuation of 20 dB.  This was to get rid of the mess near DC.  Some of the mess at DC was tracking with the signal, but some of it seemed unrelated.

I then took the envelope with the "Complex to Mag" block.

I then used a rectangular pulse matched filter with taps of $[1, 1, 1, 1, 1, 1, 1, 1]/8$ .  This introduces receiver side ISI, but reduces the noise.

I don't know how you captured this signal, but it would be better if you can do something on the analog side to improve the signal level or SNR, and also preserve the component that was likely at 18.6 kHz, since you're using a sample rate of 44.1 ksps.