#!/usr/bin/perl -w
use strict;
use CAM::PDF;
use CAM::PDF::PageText;
use File::Spec::Functions;
use File::Find::Rule;

## ... steps 1 and 2 as per OP code ...

my $outputDir = 'F:/project_italia/firm_text';
( -d $outputDir and -w _ )
    or die "Output directory $outputDir not found or not writable\n";

open(LIST, ">>", 'F:/project_italia/firmList_pdf.txt' )
    or die "Can't open destination.fil $!";


foreach (@allDir)
{
    ...
    
    foreach (@filings)
    {
       my $fileName=$_;
       my $pdf = CAM::PDF->new($_) or do {
           warn "PDF->new failed on $_\n";
           next;
       };

       ...
       
       # open output text file  (NB: ">>" appends, creates if necessary)
       open(DEST, ">>", "$outputDir/$textName[4].txt" ) or do {
            warn "Unable to append to $outputDir/$textName[4].txt: $!\n ";
            next;
       };
       ...