There are no less then three very well supported ways to program a Raspberry Pi Pico, all with a great and active community:

1. The official bare C-SDK
2. arduino-pico, based on the C-SDK, but using the familiar .ino sketches.
3. MicroPython / CircuitPython

So first thing is to decide which one to use in this project. The two main requirements are SPI input for the INMP441, and the ability to use https://github.com/kingyoPiyo/Pico-10BASE-T for sending the audio frames over Ethernet.

Funny thing is, the 10BASE-T code by kingyoPiyo is written for the C-SDK, and only arduino-pico and MicroPython have SPI input! (the SPI code in the C-SDK is output only as of yet)

So for now I have chosen to go with arduino-pico, since it should be relatively straightforward to use the 10BASE-T code as a library in Arduino. I've never done this before, so keep your fingers crossed.