Comment by miles

Here is the apparent origin post of this undocumented preference:

Hidden preference to alter the menubar spacing https://www.reddit.com/r/MacOS/comments/16lpfg5/hidden_prefe...

The author describes tracing Bartender's activity to hunt down the method.

And this blog post mentions higher values than 6 (recommending 12 for NSStatusItemSpacing and 8 for NSStatusItemSelectionPadding):

How to fix Mac menu bar icons hidden by the MacBook notch https://www.jessesquires.com/blog/2023/12/16/macbook-notch-a...