The \\B in the string literal becomes \B in the resulting string.

In a regex pattern, \B means "Match except at a word boundary".

Since the \B is between an "A" and the end of the string in the first snippet, it's on a word boundary.

Since the \B is between a space and the end of the string in the second snippet, it's not on a word boundary.

You want

$pat = "A\\\\B";
$text = /$pat/
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or

$pat = qr/A\\B/;
$text = /$pat/
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or

$substr = "A\\B";
$text = /\Q$substr\E/
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