How to troubleshoot iMac M4 (base model two-port) wired ethernet connection issues?

According to Apple, what you are trying to do won't work.

"The 24-inch iMac comes with a 143W power adapter. If your iMac has four ports, the included power adapter has built-in Ethernet. The 24-inch iMac with two ports can be configured with a 143W power adapter with or without built-in Ethernet only at the time of purchase and cannot be added later.

Note: In order to add Ethernet capabilities on the 24-inch iMac with two ports after purchase, you must use a USB-C to Ethernet adapter (sold separately)."

Take a tour of iMac - Apple Support

pjabbott wrote:

That’s crazy. I have an en0 device with its own MAC address in addition to the en1 interface for wireless. Where is the MAC address coming from if there is no networking hardware? And I can’t believe Apple would have two different hardware variants of the same spec machine.

Repeating the quote from Apple on this, the power supply with the ethernet port simply does not work with your version of this Mac, which is the base model. You can still get wired ethernet with the USB-C to ethernet adaptor, as noted by Apple and several other users who also responded. If you wanted to use that ethernet equipped power supply, you would have had to purchase a more advanced model, not the base model. It is common that lower end version of the hardware come with fewer capabilities or options. As users, we can't do anything about this other than purchase the model that has the options we want. When I got my wife's iMac, I specifically chose a model that had the option to use the power supply with the built in ethernet port -- and I had to pay more for it.

"The 24-inch iMac comes with a 143W power adapter. If your iMac has four ports, the included power adapter has built-in Ethernet. The 24-inch iMac with two ports can be configured with a 143W power adapter with or without built-in Ethernet only at the time of purchase and cannot be added later.

Note: In order to add Ethernet capabilities on the 24-inch iMac with two ports after purchase, you must use a USB-C to Ethernet adapter (sold separately)."

Take a tour of iMac - Apple Support

pjabbott wrote:

And I can’t believe Apple would have two different hardware variants of the same spec machine.

It is possible to custom-configure a new 24" two-Thunderbolt/USB4-port M4 iMac with an Ethernet port. But as steve626 pointed out:

Take a tour of iMac - Apple Support

"The 24-inch iMac comes with a 143W power adapter. If your iMac has four ports, the included power adapter has built-in Ethernet. The 24-inch iMac with two ports can be configured with a 143W power adapter with or without built-in Ethernet only at the time of purchase and cannot be added later.

Note: In order to add Ethernet capabilities on the 24-inch iMac with two ports after purchase, you must use a USB-C to Ethernet adapter (sold separately)."

That implies that there are different variants of the "same spec" machine. (If by "same" you are referring to specs other than the ones surrounding the power brick and the Gigabit Ethernet port.)

I remember that back in the Intel-based iMac days, there were some 21.5" iMacs which only came with a place to plug in a blade SSD if you ordered them with a SSD or a Fusion Drive. Order one of them with a mechanical hard drive, and Apple would save a few cents by leaving off the connector for plugging in a blade SSD. Later, when OWC came out with compatible blade SSDs, those who had originally purchased mechanical hard drives got the nice "surprise" of learning that they could install an internal SATA SSD, but could not install a faster internal blade SSD.

You bought a "price point" iMac. To get the lower price, you gave up 2 CPU cores, 2 GPU cores, 2 multi-purpose USB4/Thunderbolt ports, the ability to drive a second external display, a Touch ID sensor, and Gigabit Ethernet as a standard feature. Maybe another one of the "price point" measures was that if you did not grab the opportunity to custom-order a two-port iMac with the "Ethernet power brick", they left some small part out at the factory that the "Ethernet power brick" would need to connect to – much like with that old 21.5" iMac blade SSD socket.

An en# could be a Thunderbolt port or a Bluetooth port, not just ethernet or WiFi.

I second the suggestion made by @steve626 ... get a USB-to-Ethernet adapter. I use this one from Belkin and it works like a charm.

But they aren't the same spec machine. One is the lower end two port model and the other the higher end 4 port. While we use the ports to tell them apart, there is no telling what is different inside.