With a direct USB-C to 3.5mm jack input I believe you will only be able to record in mono on a smartphone. And the sound quality will depend on the (usually very poor) phone preamp.
There are no mic preamps or ADCs for recording from external devices in smartphones, unless it's an older phone with a TRRS jack which would accept a mono analog mic input on a set of wired earbuds. The mic preamps and converters for what is being discussed here will be in the external interface you connect.
For Android, I know many people have had success with this app in the past though I have never used it myself. The key points are: (1) you can use any USB class-compliant interface such as those you would connect to a PC, and (2) it bypasses any limitations or additional processing done when recording through Android the 'normal' way.
https://www.extreamsd.com/index.php/products/usb-audio-recorder-pro
I have used the same developer's playback app for many years, which also can directly stream to your external playback device.
https://www.extreamsd.com/index.php/products/usb-audio-player-pro
I can confirm the app you linked works perfectly and is well worth the six dollars. It records in stereo up to 16/48, monitors both channels independently and allows you to adjust gain on the fly. The resulting waveform looked good when I recorded music from my stereo.
For exact gear used, I plugged a pair of SP-BMC-2 mini mics into a sound pros SAPM-1-USB-C adaptor and then into a Samsung Galaxy S24 running USB Audio Recorder PRO. Next step is try at a show, maybe Grateful Drag in a few weeks but this looks like a serviceable rig that is very low profile