Use -p function to check if STDIN is a pipe (to read from standard input for the option; else require an argument for the option) ... 

# Some time later, changed the code to collect all the input "do { ...
+ };",
# not just the first line of STDIN.

#!/usr/local/bin/perl

use v5.26; use warnings;

use Data::Dumper qw[ Dumper ];
use Getopt::Long;


my $opt;
GetOptions( 'opt:s' => \$opt )
   or die $!;

say Dumper( { 'Initial, opt' => $opt } );

if ( defined $opt )
{
   if ( -p STDIN )
   {
      say q[Any option argument will be abandoned; collecting STDIN ..
+.];
      # Could process standard input line by line.
      # Here, all is collected at once.
      do { local $/; $opt = <STDIN> };
      say Dumper( { ' ...after collecting STDIN, opt' => $opt } );
   }
   elsif ( $opt eq '' )
   {
      die qq[Neither a value was given for \$opt, nor was specified on
+ standard input.];
   }
   else
   {
      say qq[STDIN is not a pipe; using existing \$opt = $opt.];
   }
}
else
{
   say qq[\$opt was not used, so STDIN was ignored.];
}

say Dumper( { 'Final, opt' => $opt } );

[download]

Later shoved the output of various cases under readmore ...

Missing value for the option & no pipe ... 

> perl stdin-pipe.pl --opt
Neither a value was given for $opt, nor was specified on standard inpu
+t. at stdin-pipe.pl line 25.

# This is interesting for "say Dumper ... Initial" still runs
# though "die" happens earlier.
$VAR1 = {
          'Initial, opt' => ''
        };

[download]

Only the value ... 

> perl stdin-pipe.pl --opt Value
$VAR1 = {
          'Initial, opt' => 'Value'
        };

STDIN is not a pipe; using existing $opt = Value.
$VAR1 = {
          'Final, opt' => 'Value'
        };

[download]

Option value of X is ignored in preference to standard input ... 

> date -u | perl stdin-pipe.pl --opt X
$VAR1 = {
          'Initial, opt' => 'X'
        };

Any option argument will be abandoned; collecting STDIN ...
$VAR1 = {
          ' ...after collecting STDIN, opt' => 'Wed May  3 05:44:43 UT
+C 2023
'
        };

$VAR1 = {
          'Final, opt' => 'Wed May  3 05:44:43 UTC 2023
'
        };

[download]

No value for the option, with standard input ... 

> date -u | perl stdin-pipe.pl --opt
$VAR1 = {
          'Initial, opt' => ''
        };

Any option argument will be abandoned; collecting STDIN ...
$VAR1 = {
          ' ...after collecting STDIN, opt' => 'Wed May  3 06:24:29 UT
+C 2023
'
        };

$VAR1 = {
          'Final, opt' => 'Wed May  3 06:24:29 UTC 2023
'
        };

[download]

In reply to Re: checking for piped input data by parv
in thread checking for piped input data by Anonymous Monk

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