So please clarify - what does "topicalizer" mean, and why does it make what I wrote wriong?

It means it acts much like the pronoun "it", that is, it is the implicit argument of many operators and functions. Thus

$_ =~ /$regex/;
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is always equivalent to just

/$regex/;
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but the latter is more concise, and is typically idiomatic of Perl. So it is most often more clear. If (you think) it is not, then an explicit variable name may be in order. And in that case you have to do

$var =~ /$regex/;
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But then, if you have a bunch of matches (or substitutions or ...) to do, people at times even uses a for loop just for its aliasing effect, e.g.:

s/$rx1/foo/, s/$rx2/bar/, s/$rx3/baz/ for $var;
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