This is a confusing one as the PS1 definitely has a 384 mode, yet in a discussion on the Mednafen forums about the PS1 aspect ratio the admin who I can only presume is the main dev doesn’t mention it but “366(approx.) width” when going through the supported modes.
Yet in the forum for the emulator you are currently using 384 is the mode that is mentioned.
My hunch is that the horizontal resolution is 384 but like you said the active area is another thing altogether, which is why people report 368 for Tekken 3 and X-Men vs SF.
368 would also not draw into the overscan area like 384 does, you crop 8 pixels from each side so that could well be why that visible area is used.