The CPU upgrade had nothing to do with it.
The user interface of Plex HTPC is designed with a fixed aspect ratio of 16:9. It will not flex for other screen ratios.
4096x2160 would be an aspect ratio of ~17:9
So seeing black bars at the side is very much expected.
The aspect ratio during video playback is a different topic:
By default (i.e. Zoom in HTPC’s settings is set to “Normal”), the actual video picture is always using all pixels which are available. At least as far as it is possible without either cropping the picture or stretching it un-proportionally.
This would automatically zoom into FHD content, when playing on a 4K screen.
If your content does have black bars as part of the video (many movies are stored that way on Bluray), you may find the need to zoom in further during playback.
If your screen is actually 17:9, you will by default even get black borders at the sides if you play 16:9 content that doesn’t have black borders encoded in the picture.
(the alternative would be to transcode the video and crop off all black borders while doing so).
See Use `mpv` features which are not exposed in Plex for Windows/Mac/Linux and Plex HTPC for a method to define keys for the zooming during playback.
post scriptum: after enabling automatic resolution switching in Plex HTPC, thing can sometimes work differently. You should definitely experiment with that option.
Activating it does leave the work of upscaling of lower-resolution content to the TV, otherwise Plex HTPC will do it. Depending on both the abilities of your TV device and the GPU in your computer and the video quality setting in Plex HPTC, picture quality can differ.