> > Obviously Perl needs to escape the backslash inside a regex

> not after interpolation of variables like $bs

I have to correct myself, it depends on the side of the substitution

• the right side is a simple doublequoted string, so after interpolation no escaping
• but the left side is a regex with two levels of escaping
  1. string interpolation with escaping first, i.e. \$bs won't be interpolated
  2. regex interpretation with escaping first, i.e. /\*/ is not a quantifier but literal * same with /$bs*/

compare

d:\>perl -E"for $x (qw/C:\berrybrew\test C:\berrybrew /) {$_=$x; $bs=c
+hr(92); s#$bs$bs#<${bs}>#g; say}"
C:<\>berrybrew<\>test
C:<\>berrybrew

d:\>
[download]

or to eliminate the Win command line

use v5.12;
use warnings;
use Data::Dump;

my $bs=chr(92);

for my $x (qw/C:\berrybrew\test C:\berrybrew /) {
    $_=$x;
    s#$bs$bs#<${bs}>#g;
    say;
    #ddx $_;
}

$_='$bs';
s/\$bs/<$&>/;
say;
[download]

C:<\>berrybrew<\>test
C:<\>berrybrew
<$bs>
[download]

so this might be the OPs original problem

see also

s/RegEx/substitutions/: Variable interpolation and when to use /e - modifiers