Why doesn't <STDIN> initialize and fill $_ in the following control block?

Because <STDIN> never changes $_.

while (<$fh>) { ... }
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is short for

while (defined($_ = <$fh>)) { ... }
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But since you don't have something of the form

while (<$fh>) { ... }
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you never assign anything to $_.

while (<STDIN>) {
   s/\s+$//;
   last if /^(?:exit|quit)?$/i;
   ...
}
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