Thank you! I am surprised it doesn't work with iPad Pro. They don't ship to Germany, otherwise I'd buy one and try. If you have an ESP32-S3 device, I can help you with it if it doesn't work.
https://www.amazon.de/6-35mm-Microphone-Recording-Electronic...
I don't know why this one would work and the other not, but my guess will be that this one has a chip that doesn't offer up a disconnected output device as well (which would be my totally uneducated guess as to why my iPad hates the other cable and the Mac, which has switchable output devices, doesn't)
There was an ESP32 board I wanted to try (below) but it looks like it's a 1.8" sibling of the one you are using so maybe I'll just track down the one you're using.
https://thepihut.com/products/esp32-s3-development-board-wit...