If you wanted to use Unicode's definition of case insensitivity — they are the experts in this area — you should convert the strings to fold case (not lower case or upper case) and then compare them. The simplest way of doing that is:

$s1 =~ /^\Q$s2\E\z/i
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Like the lc and uc methods, this assumes the string has previously been normalised. All together,

use Unicode::Normalize qw( NFC );

$s1 = NFC($s1);
$s2 = NFC($s2);
$s1 =~ /^\Q$s2\E\z/i
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