modern perls have optimisations to avoid recompiling patterns if the interpolated variables haven’t changed

Modern perls are even smarter than that. They look at the string after interpolation, and if that's the same, the regex isn't executed:

$ cat xx
#!/usr/bin/perl

use strict;
use warnings;

foreach my $x (["foo", "bar"], ["fo", "obar"]) {
    my ($foo, $bar) = @$x;
    "" =~ /$foo/;
    "" =~ /$foo$bar/;
}
 
__END__
$ perl -Dr xx 2>&1 | 
  perl -nle 'if (/EXECUTING/ .. eof) {print if/^Compiling/}'
Compiling REx `foo'
Compiling REx `foobar'
Compiling REx `fo'
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Perl won't recompile the second regex, since while the values of both $foo and $bar have changed, the value of "$foo$bar" hasn't.