My interpretation is that printf makes variable substitution before format the output. This means that in:

printf"$a[%d]\n", 4
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$a[%d] is interpreted before %d, then warns. The same happens in the second example

In the last one:

perl -wle 'my @a=1..9; printf"\$a[%d]\n", 4'
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Because the $ is scaped, there is no variable substitution and the format process behaves normally

citromatik