The menu jumps a few pixels after the website loads

I like to call that “Fix it with JavaScript” aka “Fix it in post“. It happens when a someone can’t do something with CSS so they resort to JS. On a slow-loading site, such as the one you linked, the time it takes to load the JS is long enough so that any corrections to the display are visible to the human eye.

You can either fix the underlying display issue in the CSS so the JS doesn’t have to do anything, fix whatever is causing the site to load so slowly so that the change is imperceivable, or live with the momentary flicker.