Seems like you're pretty close, but you're making it harder than it needs to be. Also, it sounds like you want to output just the first line that is found for a given url, but your code will always preserve the last line for a given url.

Here's a simpler version that preserves the first line -- I'm including the input data with the script (you'll be reading it from a file), and I'm just printing the output to STDOUT (you can open an output file, or just redirect stdout when you run the script):

use strict;
use warnings;

my %file_hash;
my @lines = <DATA>;
    
for my $line (@lines)
{
    chomp($line);
    my ($name,$url,$text) = split('@',$line);
    $file_hash{$url} = $line unless ( $file_hash{$url} );
}

for my $key ( sort keys %file_hash )
{
    print "$file_hash{$key}\n";
}

__DATA__
name1@url1@text1
name1@url1@text1
name1@url1@text11
name2@url2@text2
name2@url2@text21
name3@url3@text3
[download]

(BTW, this sort of thing would normally be done using while(<>) to read and process the input data one line at a time, rather than reading the whole file into memory and then looping over it with for my $line (@lines) -- but it's not a big deal in this case.)

You might be interested in looking at this command-line utility: col-uniq -- remove lines that match on selected column(s). It would produce the output you want from your particular input file like this:

col-uniq -d '@' -c 2  input.file > output.file
[download]

But in order for that to work, you'd need to make sure the input data was sorted according to the url field, whereas the input doesn't need to be sorted for the snippet above to work.