The fact that, for 0 <= $i < @arr, $arr[ $i ] == $i makes @arr irrelevant (so the solutions you received before the correction are still valid). But for the general case where this equality does not hold

print join ',', @arr[ @vals{ sort { $a <=> $b } keys %vals } ];
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...though I think code should be easier to read than that. I would break that up a bit; e.g.:

my @sorted_keys = sort { $a <=> $b } keys %vals;
print join ',', @arr[ @vals{ @sorted_keys } ];
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