Need audio (not headphone) out for new iPhone

I have an apple audio adapter with a male lightning going to female usb (a) and female lightning charger out port.

Plugged into the usb A out port is a good/audiophile usb cable to DAC. I would like to continue using that good-cable-to-DAC setup.

I got an apple Female lightning to male USB C to be able to use that adapter with my new iPhone 16 and two iPad Pros. (ie. the new adapter is piggybacked to the original adapter)

But when I tried that setup it said that accessory is not supported and just sent the sound out of the iPhone speakers instead of the paired-adapter setup.

How can I run the audio through my good USB cable and DAC? Not finding a usbC Male to usbA female audio adapter anywhere. It would be nice to also have the charger function but not mandatory.