Can't do ethernet tethering while (wireless) charging the phone

I have a Google Pixel 4 XL with Android 12 stock OS, and I'd like to use it for ethernet tethering (for devices not supporting wifi). I'd also like to concurrently keep this type of tethering enabled and charge the phone when needed. However, because I can't charge it via USB-C cable while already connected to a RJ45 cable (though I'm using an adapter), I thought wireless charging, since it is supported, could solve the problem. But unfortunately it disables and blocks tethering until I put the phone off the wireless pad and re-plug the adapter. Is there a way to fix this (through Developer Options or else)?