The command argument to Net::OpenSSH methods must be a system command (e.g. ls, grep, etc.). You can not pass perl code there.

In your particular case, you can use SFTP to query the remote filesystem:

use Data::Dumper;
my $sftp = $ssh->sftp;
my $stat = $sftp->stat($remote_file);
print Dumper($stat), "\n";
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