If I correctly understand the question, you don't need sprintf for this at all, but in the substitution you need a double eval, and a corresponding double layer of quoting:

% cat t0
use strict;
use warnings;

my $input = 'foo.ra';
my $find = '\.(.)(.)$';
my $replace = 'b$2$1s';
printf qq{result "%s"\n}, replace($input, $find, $replace);
exit 0;

sub replace {
  my($input, $find, $replace) = @_;
  $input =~ s{$find}{qq{"$replace"}}ee
      or die "input did not match";
  return $input
}
% perl t0
result "foobars"
%
[download]

The first eval creates the string "b$2$1s", the second eval then works out that that should be "bars".

At a brief glance your (type 2) sprintf solution could probably also be made to work, but would also need a double eval and will get rather complicated. So I would not recommend pursuing that approach further other than as a learning experience.