With adjectives, some adjectives are gradable: there are degrees of goodness, so something can be fairly good or very good. Others are ungradable- something is either finished or not: it can't be very finished.
The same is true with intensifier adverbs: if very means 90%, you can intensify if further by saying very very to mean 99%. It's not wrong to say extremely extremely, but extremely comes from the latin word extremus, meaning outermost - you can't go any further- so we can think of it as meaning 100%. You can't get higher than that, so there's no point, unless your intent is to be over-dramatic.
According to this NGram graph, extremely extremely
was relatively common pre-1820. It looks like has made a comeback since 2010, but most of the instances seem to be tabulated responses to questionnaires, where the word extremely occurs in two or three successive answers.
'There was a little girl, who had a little curl Right in the middle of her forehead, And when she was good, she was very, very good, But when she was bad she was horrid.'
– Edwin Ashworth Nov 19 '21 at 11:29