If you have do not have another tv to test the Premiere on, I think you have exhausted what can be done on the Premiere itself. (It still could be the Premiere unit itself, but without testing it on another TV, no real way of ruling it out.)
Now you are left with seeing if there are any settings within the TV itself that can be contributing. It would likely be under the Video or HDMI options under your TV Menu settings. There may be a Resolution or Display Setting mismatch. There is also a manual Factory Reset option depending on model.
If you can provide the actual model number of your TV, would be able to look into it a little bit further. The standard troubleshooting for Bravia did not show the actual pixelation you are experiencing so it did not show a standard solution step. Here is kind of where you try to plug in a DVD player, or a laptop via HDMI cable or change the HDMI cable itself to see if you are getting similar results to the Roku.
For some of the Bravias, there is a custom mode and standard mode. Standard is usually fine, but in custom you can turn off a lot of advanced settings, eliminate noise, enable HDR.
Kind of down to determine if the Premiere or the TV itself is the problem. Process of elimination through different tests. Other option is to pick up another Premiere at Walmart or Best Buy and just plug it in. If same results, then you now know it is TV related.
Take a look at this link (not model specific) but does a general walkthough of using Bravia with attached devices and the seeting you may have to change. The link is actually page13, so read through his article and see if any of this is helpful. Note the settings you may have to make at each HDMI connection to make a device function. https://www.tomsguide.com/us/sony-tv-settings-guide,review-5605-13.html
Roku Community Streaming Expert
Just another Roku user... I am not a Roku employee.
Insignia RokuTV, Ultra 4660x, Premiere+ 3921, Express 4k+ 3941