Perl: replace literal expression and literal variable names

Looking at the documnentation for \Q in man perlop:

For the pattern of regex operators ("qr//", "m//" and "s///"), the quoting from "\Q" is
applied after interpolation is processed, but before escapes are processed.  This allows
the pattern to match literally (except for "$" and "@").  For example, the following
matches:

   '\s\t' =~ /\Q\s\t/

Because "$" or "@" trigger interpolation, you'll need to use something like
"/\Quser\E\@\Qhost/" to match them literally.

And, checking the doc for quotemeta (which is used to implement \Q ... \E internally) in man perlfunc:

Beware that if you put literal backslashes (those not inside interpolated variables)
between "\Q" and "\E", double-quotish backslash interpolation may lead to confusing
results.  If you need to use literal backslashes within "\Q...\E", consult "Gory
details of parsing quoted constructs" in perlop.

Because the result of "\Q STRING \E" has all metacharacters quoted, there is no way to
insert a literal "$" or "@" inside a "\Q\E" pair.  If protected by "\", "$" will be
quoted to become "\\\$"; if not, it is interpreted as the start of an interpolated
scalar.

So the $ can't be kept inside \Q ... \E. You'll have to do something like:

% echo '...${var}#other.([]);,=${var}#other${var}...' | perl -pe 's/\Q.([]);,=\E\$\Q{var}\E/.([]);,=ok/'
...${var}#other.([]);,=ok#other${var}...