During fullscreen playback (in my case fullscreen youtube playback in Safari), the system OSD automatically centers perpendicular to the top of the display.
However, in BetterDisplay's replica OSD, it does NOT center the same way.
Here's a visual example:
System OSD

BetterDisplay's OSD (we can observe its OSD still lines up with the menu bar icon)

(ignore dingus in the background)