Use the -s test:

use strict;
use warnings;

for my $file (qw/bar.txt barwithdata.txt/) {
    next unless -s $file > 114;
    print "file $file has data\n";
}
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Note that 114 is the number for my O/S. Yours may differ due to different EOL/EOF patterns.

One way is to count the number of consecutive lines that start with a +- or += (just in case for some reason you have normal lines that start with a +. Hopefully legit lines won't start with += or +-. If they do, you'll have to lengthen the regex). If you get more than one, the file is deemed empty and we skip it. Note I skip the lines that have the separators and don't print them.

use warnings;
use strict;

my @files = qw(a.txt b.txt);

for my $file (@files){

    open my $fh, '<', $file or die $!;

    my $sep = 0;

    print "working on file $file\n";

    while (<$fh>){

        if (/^\+[-=]/){
            $sep++;

            if ($sep > 1){
                print "skipping $file\n";
                last;
            }
            next;
        }

        $sep--;

        chomp;
        print "$_\n";
    }
}
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file a.txt:

+=======+=======+============+============+============+
+-------+-------+------------+------------+------------+
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file b.txt:

+=======+=======+============+============+============+
line 1
line 2
+-------+-------+------------+------------+------------+
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output:

working on file a.txt
skipping a.txt
working on file b.txt
line 1
line 2
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Use the directory functions: opendir, closedir and readdir.

opendir DIR, $dir or die "cannot open dir $dir: $!";
my @filenames= readdir DIR;
closedir DIR;
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You can use the scalar Range Operators

open my $fh, "<", $file or die $!;

while (<$fh>) {
    print if /+=======+=======+============+============+============+
+/ .. /+-------+-------+------------+------------+------------+/;
}
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use flag like below,

foreach my $file (@filenames)
my $filepath = "/FILEPATH/$file";
open my $fh, "<",$filepath or die("could not open log file: $!");
my $in = 0;

while(<$fh>)
{
    $in = 1 if /+=======+=======+============+============+===========
+=+/;
    print if($in);
    $in = 0 if /+-------+-------+------------+------------+-----------
+-+/;
}
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And how, precisely, do you expect to determine that any given file "is missing the data" without reading it?

The answers above tell you how to read files and determine whether they have the format shown in your last snippet... but that is NOT the same as ascertaining the presence or absence of data without reading your files.

My bad . I should rather put it as skip reading the file further