The module is documented to do that:

All of the data calls return a response hash containing the keys url, message, warning, filename and error. Normally only url and filename will be interesting to you; however message can contain extra information and will be printed if verbose is set to 1, warning can contain warnings from the server and is always printed with warn(), while a value in the error key triggers the module to die.

So, maybe you want to wrap the calls that can fail within eval { ... } and inspect the value you get back from the call?

use Data::Dumper;

my $response;
my $ok= eval {
    $response= $plotly->plot( ... );
    1
};
if( ! $ok ) {
    warn "Plotly error:";
    die Dumper $@;
};

...
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