Views view unformatted and outputting taxonomy custom field
Finally got it to work!  Here is how you do it.  Assuming your field is called field_category.  My template is called views-view-unformatted--my_view_id_name.html.twig.

{% set my_category_id = row.content['#row']._entity.field_category.0.target_id %}


It does seem pretty silly to me that it has to be that long.  It would be very cool if it was something more like this and that all values associated to a post (since that is what is being output) are available and exposed to the view.

row.content.field_category.id


And if all taxonomies that are added would follow the same path.  Seems unneccesary to have it in #row, then in _entity, then needing to add a 0 and use some oddly named thing called target_id.

I'm new to Drupal coming from Wordpress.  There are nice clean functions in wordpress for getting taxonomy ID and names.  Not too many hoops you need to jump through.