Then you can run then in parallel combining Net::OpenSSH::Parallel and Net::SFTP::Foreign:

# untested

my @host = ...;
my $dir = ...;

use Fcntl ':mode';
use Net::OpenSSH::Parallel;
use Net::SFTP::Foreign;

my $pssh = Net::OpenSSH::Parallel->new;

for my $host (@host) {
  $pssh->add_host($host);
}

sub sftp_rename {
  my ($label, $ssh) = @_;
  my $sftp = $ssh->sftp;
  $sftp->find($dir,
              ordered => 1,
              wanted => sub {
                my (undef, $entry) = @_;
                if (S_ISREG($entry->{a}->perm)) {
                  my $fn = $entry->{filename};
                  $sftp->rename("$fn", "$fn.bak");
                }
                0;
              },
           );
}

$pssh->all(parsub => \&sftp_rename);
$pssh->run;
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