It's hard to tell (since the issue is really on the server side). But it sounds like either the server wants the data to be form-data (labelRequestXML=<longstringofxml>) or it's doing different processing based on the the content-type. You can try setting the type:

#!/usr/bin/perl 

use strict;
use warnings;
  
use LWP 5.64;
my $browser = LWP::UserAgent->new;

my $xml= qq[<?xml version="1.0" encoding="utf-8" ?>
.... snip ....
];
  
my $url = 'https://www.envmgr.com/LabelService/EwsLabelService.asmx/Ge
+tPostageLabelXML';

my $response = $browser->post(
  $url,
  Content_Type => 'text/xml',
  Content  => $xml
);

print $response->content;
[download]

or if it wants form data

my $response = $browser->post(
  $url,
  Content => [
    labelRequestXML => $xml
  ]
);
[download]