Raspberry Pi + Microcontroller for commuting audio input and output (audio matrix switch)
You need a switch matrix made of relays or analog muxes to connect a specific source to a specific (or many) targets. A simple MCU can do that.

If you have to do ADC conversion of each input, RPi can be more of a help.
Possibly you need external ADC with proper sample rate and bit depth and multiple channels. You also need multiple DACs.

But, I do not see sound to digital and then back to sound conversion if there is no need for digital processing.