You need to convert the delimiter into a regex pattern that matches the delimiter. That's what quotemeta does.

my $pat = quotemeta($delim);
s/$pat/\\$delim/g;
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quotemeta can be accessed with \Q..\E in regex literals (among others).

s/\Q$delim\E/\\$delim/g;
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or

s/\Q$delim/\\$delim/g;     # \E is optional at the end of the literal.
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