I think this problem can be simplified by thinking about the file as multi-line records. Change your record separator to '>>' and process only the records meeting your threshold. Be sure to include the 'm' at the end of the regex for multi-line matching.

my $threshold = <STDIN>; # or so...
my @records;

{
    local $/ = ">>";
    while (<FASTA>) {
        if ( /(\d+\.\d+)% identity/m ) {
            push @records, $_ if $1 > $threshold;
            # - or -
            # process($_);
        }
    }
}

# @records now holds lines meeting threshold
# process as needed...

# - or -
# sub process { ... }
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