Was looking at some emu docs and like Mednafen both Xebra and Nocash make no mention of 384 at all, only 368. This is also reflected in the width option that Xebra allows you to select from in the video options.
http://drhell.web.fc2.com/ps1/
https://problemkaputt.de/psx-spx.htm#graphicsprocessingunitgpu
The Nocash one is interesting as 368 is set apart from the other horizontal resolutions but I’m not bright enough to parse the rest of the text beneath it to work out why!
The weird thing is that emulator docs seem to always mention 368 but more general overviews like the below always mention 384 instead.
https://www.zophar.net/fileuploads/2/10731bgqkx/playstation.htm