"Can't use string ("") as a HASH ref while "strict refs" in use

That error results from trying to evaluate an empty string as a hash reference.  In other words, the part you have in between %{...} most likely evaluates to the empty string, instead of the hashref that would be needed here:

use strict;
use warnings;

my $data = {};
$data->{foo} = { a => 1};
$data->{bar} = "";

if ( %{ $data->{foo} } ) { ... }   # ok, because $data->{foo} is a has
+href
if ( %{ $data->{bar} } ) { ... }   # not ok, because $data->{bar} is e
+mpty
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Best is probably to directly test whether the value in question is a hashref, i.e.

if ( ref($data->{bar}) eq "HASH" ) { ... }   # ok, even if $data->{bar
+} is empty/undef
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or, adapted to your example:

    ...
    next unless ref($coordinates->{$group}{$id}{$stage}{"coords"}) eq 
+"HASH";

    # print individual and coordinate information
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See ref.