Wordpress theme hierarchy problem

I am running Wordpress on localhost (with MAMP) and in parallel I have my own server with I think the same config for wordpress.

Issue: I created in PG a Wordpress page which works perfeclty on localhost.

If I copy the whole theme to my domain then instead of the single-customposttype.php it renders index.php which I cant find why it does that.

So I have a custom post type called: kunstwerken defined like this, I did not define it in CPT plugin.

Then I have a HTML page that exports to:
single-kunstwerken.php

And “kunstwerken” (custom post type) has the taxonomies called Art

like this:

And Arts has the categories: 3D, installation, Painting, Photography
defined like here:

So then..
I have a menu link to Painting so it should show all paintings:

URL like: localhost/showpage/art/painting/
So I have then my HTML that exports in PG to single-kunstwerken.php
When I preview in localhost I get this page.
But on the external domain page (the www server) I get the contents of index.php while all the same files on localhost are on the www domain.

Why is WordPress going to index.php? following WP’s hierarchy I don’t see what I am doing wrong.

help appreciated

My structure’s idea is copied from a course from @adamslowe , same sort of setup