Most USB-C to Ethernet adapters rely on the USB signal from a USB-C port, and so I'd expect them to work with any of the M3 iMac's USB-C ports (Thunderbolt or not). For instance, if you look at the compatibility list for
The Belkin USB-C to Gigabit Ethernet Adapter - Apple
it includes "MacBook (Retina, 12-inch, Early 2015 – 2017)" (Macs which don't have Thunderbolt, only USB-C). A hint that the device doesn't require, and probably doesn't even understand, Thunderbolt.
An example of a Thunderbolt 3 to Ethernet adapter would be the OWC Thunderbolt 3 10G Ethernet adapter. If you were getting that one, you would need to attach it to one of the M3 iMac's Thunderbolt 3 ports.
https://www.owc.com/solutions/thunderbolt-3-10g-ethernet-adapter