Sparky looks like fun!
As mentioned earlier, I am part of the Tympan team, who were funded to make an open source hardware and software platform for audiological research (ie, hearing aids and whatnot). We have a lot of overlap with what you're doing, which is cool!
A custom hearing aid solution. Meet Tympan, an open source hearing aid product. Audio software and hardware combined.
www.tympan.org
We've been at this for years. Our hardware is at rev F. It's built around a Teensy 4.1. The analog audio portion is built around a TI AIC3206. It has two MEMS mics on the PCB, or accepts external microphones.
We also have earpieces that connect to the Tympan. The earpieces are similar to behind-the-ear hearing aids. These earpieces use digital PDM microphones. The use of digital MEMS mics is very common these days. They are probably as quiet as you're going to get in a small low-cost device. To get quieter, you'd probably have to move into highly specialized microphones. We use the Invensense IM69D130 mics, but there might be even quieter ones out there now.
PDM mics cannot connect directly to the Teensy; they need some sort of interface chip [stricken due to being corrected in a responding post below. Cool.]. Luckily, our AIC3206 provides a PDM interface in addition to all of its analog inputs...so, using PDM mics was pretty easy for us.
If you choose to stick with analog microphones, and if you think you're limited by the noise floor of your analog preamplification, don't get fooled by the single-number values advertised as the self noise for the op amp. Those single-number values are usually for the self-noise at a frequency way above audio frequencies. At audio frequencies, the noise level can be different, sometimes radically so [*].
Instead, you'll need to dig into the datasheet, find the graph of noise versus frequency, and see what the noise level is down at audio frequencies. That'll tell you what you need to pick the best op amp for your needs.
Chip
[*] For a while, I was focused on seismic signals and infra sound signals, so I needed low noise around 1-10 Hz. Op amp self-noise definitely gets weird down there. So, for sure, I had to dig into the datasheets to get frequency-specific noise values to find a good one for that use. But at a normal audio frequency of, say, 1 kHz maybe my disillusioning experience is less true...maybe the noise at 1 kHz isn't too far off from the single-number values that are advertised. To be sure, I'd suggest that you a look at the noise-per-frequency graphs in a couple of datasheets and see!