@KCog
The only Roku Premiere model that has ethernet is/was the Roku Premiere+ 4630. Any other model number of the Premiere/Premiere+ is wireless only (no ethernet capability.)
Other than the Ultra (and newer Ultra LT models) which provide for ethernet built-in to the Roku device, you can now use an USB ethernet adapter with the new Roku Express 4k/4k+ models. (ethernet adapter has to be USB 2.0 and basically 10/100, not 10/100/1000). The Streambars are similar with respect to this ethernet adapter as well.
More info on the ethernet adapters can be found here. (https://support.roku.com/article/360058027813)
Just make sure you get a USB 2.0 ethernet adapter with the specified chipsets in the article and you should be good to go if you go this router rather than purchasing an Ultra.
Just to clarify all the above...The ethernet when plugged into the TV directly is not sharing its ethernet capability with your Roku device.
Roku Community Streaming Expert
Just another Roku user... I am not a Roku employee.
Insignia RokuTV, Ultra 4660, Premiere+ 3921, Express 4k+ 3941, Streambar 9102