Uploading multiple files to server with PHP and JavaScript
The approach
In the beginning of this answer I would like to make a distinct note which is a bit off the actual code review.
You need to change your priorities in writing a code. For the moment you are focused  more on the SEO part, trying to provide PHP users with reference answers to common questions. That's a good goal per se, either for the users and for your own good, but it shouldn't overshadow the main purpose of the code - to perform a certain task. In short, you need more practice with using a code you share with other people. I would even say that your intent should be first to solve the actual problem you have at hand and then share your experience, not just decide to write a reference answer out of the blue.
I took a liberty to make this note because it makes the actual impact on the code you write, particularly in regard of the error handling.
Error handling
There are two kinds of errors, &quot;business logic errors&quot; that aren't actually errors but rather regular cases handled by the application, and &quot;real&quot; errors that occur unexpectedly and have to be fixed by a programmer.
Such errors like 'Extension not allowed' or 'File size exceeds limit' are not real errors. That's just business logic-related conditions, whose results have to be conveyed back to the user in order to let them to fix the issue on their side. But you are bluntly catching them and writing into error log where they hardly help anyone. I assume this logic is the direct consequence of your approach. Were you try to use your own code in a real life application, this flawed error handling would become immediately apparent.
So in order fo fix this issue first create a distinct kind of exception
class FileUploadUserException extends Exception {}

it will let you to catch only this particular kind of exception:
       } catch (FileUploadUserException $e) {
            $errors[] = $e-&gt;getMessage();
       }

whereas real errors have to be handled elsewhere, either in the dedicated handler or at least a global try catch around the entire application code as it makes no sense to write a repeated error_log call in every distinct chunk of code.
Another approach would be to avoid exceptions at all and use that $errors array you were intended to use at first.
Security
I would remove htm files from the list as it's a clear XSS attack on your own site.
I would also consider not using the original filenames as they would create a real mess with all sorts of weird characters and possible overwrite each other. The simplest solution would be just md5() from the file contents.
Usability
There is one simple trick that could greatly simplify the handling code. Instead of naming your field name as files[], make them enumerated, like files1, files2, ...
it will let you to handle them the most natural way using foreach, eliminating the need of count() call, a counter and even distinct variables to hold certain values from $_FILES array:
$extensions = ['jpg', 'jpeg', 'png', 'gif', 'html', 'txt', 'pdf', 'doc'];

foreach ($_FILES as $file) {
    $file_ext = strtolower(end(explode('.', $file['name'])));
    $destination = $path . $file['name'];
    ...
    move_uploaded_file($file['tmp_name'], $destination);
}