Looking at the exploded views of the Argon One case, which is initially very attractive, on online seller sites, none of them showed how the USB-C power port on the RPi board was connected to the power port on the back panel of the case. It turns out that the short answer to this seems to be that it isn't.
A German reviewer of the Argon One, Bengt Steinhauser, on an Amazon seller site pointed out the following in his review:
"To power your Raspberry Pi 4 the power connector connects using the GPIO pins and not by connecting to the USB-C port. The USB-C port remains unused inside the case. This approach has a fatal drawback: If you planned on establishing an ethernet connection via USB-C, it can‘t be done anymore. The data is not transferred via GPIO.
For me this breaks a crucial feature of the Raspberry Pi 4."
Would you regard this as 'fatal' as Bengt says? Or could you do a simple work-around by using a male-female short extension USB-C cord from the RPi board to the power port hole in the case, after unsoldering the Argon One port?