In your loop "foreach my $file (@files)" -- $file will have the name of the XML file, not the contents of the file. As mentioned above, you need to read the contents of each file and use the s modifier on the regex to make the . match newlines:

my $xml_dir = "c://temp";

opendir(DIR, $xml_dir);

my @files = grep { /\.xml$/ } readdir(DIR);
closedir(DIR);

foreach my $file (@files) {
    
    open my $fh, "$xml_dir//$file" or die "can't open $file: $!";
    local $/;
    my $contents = <$fh>;
    close $fh;
    
    print "$file is ";
    if($contents !~ /<order>(.*)<\/order>/s){
        print "NOT ";
    }
    print "valid\n";
}
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Results:

invalid.xml is NOT valid #this is your sample file 2

valid.xml is valid #this is your sample file 1