I usually avoid embedding such things in strings, for precisely the reasons you give, although where I put them would then become a matter of convenience, so my version of your code would look something like:

use strict;
use warnings;
#...
print STDERR join( "\n", $self->{Find}->{baseUrl},
                         $self->{confCode},
                         $self->{db},
                         $self->{Find}->{userName} )
           . "\n"; # assuming you wanted a trailing "\n" too
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