I have a Mac Pro (2019) and the Ethernet I/O is not working

I have a 10G Ethernet PCIe slot card very similar to the 10G ethernet used in the newer macPro and Mac studio. Also, one of the two built-in (slower on my older Mac Pro) has a cable connected and is working as an additional Ethernet port. The second built-in has no cable connected. But both of the built-ins show in this pane:

...

The Ethernet interface on this Mac Pro (and the Mac Studio as well) does not DO 100 M bits/sec Ethernet, and does not work with cables with fewer than four pairs of wires or any broken wires in them. In addition, if the connector pins are mis-aligned, that counts a broken wire and also will not work.

Although it is unusual for you to have equipment that is not capable for at least Gigabit speed internet, bad settings could make your connected equipment limited to less than Gigabit speeds, and therefore not inter-operable.

The reason 100 and slower are excluded is that up to 100 M bits/sec Ethernet uses a baseband signal (one bit per signaling interval). That only requires connected equipment go 100 M bits/sec to connect. That is also supported by only two pairs of wires in the four-pair cables.

Gigabit and higher use only a modulated signal (multiple patterns per signaling interval), which requires the extended spectrum provided by four pairs of wires to run reliably at up to the rated 100 meters of cable.

It is unlikely that the high speeds and non-trivial protocols of Gigabit Ethernet would be supported directly by the T2 chip alone. I would expect your listing to show an Aquantia 107 or 113 interface chip.

That suggests that the built-in Ethernet INTERFACE is not in the list of Network interfaces.

does it show in the list at

system settings > Network?

if you click on the PLUS [+] button under the list of interfaces, is an additional Ethernet interface available to be added?

that is fairly likely to be a hardware problem.

can you run the diagnostic?

it finds only GROSS problems, but if it DOES find an Ethernet problem, it makes getting it fixed MUCH simpler.

Unfortunately, the diagnostic tends to be a 'one size fits all' program, so when an interface is completely missing, it does not get tested and does not 'fail'.