I believe that the general convention in both British and American English

though I'm sure that it's not consistently followed everywhere

is to use "the other guy's" spellings for proper nouns for things that were named on the other side of the Atlantic. Like, we in the US will normally refer to the British "Labour Party", even though that's not how we spell "labor".

goes looking for a British movie poster for Terminator 2

This says that it's a British poster, and it has no "e":

https://www.vintagemovieposters.co.uk/shop/terminator-2-judgement-day-movie-poster-5/

You likely want to choose an example where the term isn't part of a proper noun.

i thought it was just an AmE thing. apparently it’s also common in some british regions. outside of these regions (including the entire commonwealth) it’s “judgement” which is also what my phone keyboard gives me.