I can tell you there is no setting that has to be made to Dolphin. I have a HD monitor that uses the HDMI output and Dolphin runs just fine. Maybe because your tv is older and you might be trying to force a resolution it can't handle? Since my monitor handles up to 1080p, I don't set any resolutions higher than that because it can slow things down and cause a lag. You might want to try lowering the resolution in Dolphin and seeing if that helps
Windows 11 Home x64
Intel Core i7-10700
Nvidia Rtx 2060 6GB
32.0 GB DDR4 RAM
Intel Core i7-10700
Nvidia Rtx 2060 6GB
32.0 GB DDR4 RAM