How about putting a string of microphones around the room, say at the top walls? You can get I2S microphones (here's a breakout for one [1]), so you'd just need a bundle of 6 wires running around the room.
That breakout is $6.95 with price breaks to $6.26 at 10 and $5.56 at 100 which is probably a bit pricey for this application, but really you only need the breakout to make it easy to play around with it on a breadboard. The other parts on the breakout besides the microphone module itself are just a couple of resistors. The module itself looks like it would be reasonable to solder wires directly onto, so you should be able to build a microphone string with just the microphone modules, the wire, and a couple of axial resistors at each microphone.
Here's that particular microphone module at Mouser [2]. $2.64 for one, price breaks to $2.19 at 10, $2.02 at 25, $1.90 at 50, and $1.78 at 100.
There are other I2S and I2C and SPI microphones. The SPH0645 just happened to be the first one I found to use as an example.
I'm not sure though if any of these interfaces have enough bandwidth to support enough microphones simultaneously for this to work. You might need multiple parallel strings, or maybe a hierarchical system, like having some ESP32 modules on the walls too, with each ESP32 handling a smaller string of microphones, and the EPS32s reporting what they hear along with timing data wirelessly to whatever is doing the processing.
[1] https://www.adafruit.com/product/3421
[2] https://www.mouser.com/ProductDetail/Knowles/SPH0645LM4H-B?q...