When "template name" view filter is not "required", the "any/all" option is showed twice

I'm not sure I see this issue. I only see "ANY" as an option once regardless if it is required or not.

If we were to be a bit more precise, we'd probably do a detection of the filter being required rather than just removing it altogether.

More like this:

$is_required = $this->options['expose']['required'] ?? FALSE;
    if(!$is_required) {
      $options[0] = $this->t(' - Any -');
    }

Why not simply let Views handle it?

It works perfectly fine on my instances on Drupal 10.2.3 and 9.5.11.

Here is what I get when I don't make the filter required: