Or you could change the "input record separator" and use the diamond operator <>

use strict ;
use warnings ;

my $filename = 'file.fasta';
 
open my $fh, '<', $filename or die "Could not open file" ;

my @chars ;
{
    # Calling local $/ sets the input record separator in this block
    local $/ = '>' ;
    while(<$fh>) {
        chomp ;
        push @chars, $_ ;
        
    }
}
for ( @chars ) {
    chomp ;
    print $_ . "\n" ;
}
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Output not verified (because of the leading space)

edit: One thing though, the first element in the array does not contain a result this way.

edit 2: Changed the open statement