One thing you didn't answer was whether the View would be displayed on all clinic posts, some of them, or just the one.
I tried to get this working on your site with a new template and View, and it proved a frustrating experience. Frustrating and ultimately unsuccessful.
One thing to be aware of generally with dynamic sources is that the current post (when you design the output of a View it may output many posts, but the first one is used to specify the design and is used as the source for the sample data) must actually have a value for the field you are trying to set as source.
So for the Image block, you can only set Featured Image as the source if the current post has a featured image.
It is a potential gotcha, and I did stumble across some employee posts that do not have a featured image, but even when ensuring that the first post returned by the View does have a featured image, I still ran into the same problem of being able to specify it as a dynamic source.
So I resorted to creating a View with the legacy editor. That doesn't try to generate live previews as you are editing, and is more robust.
I had no problem creating such a View, which I inserted at the end of the post with ID 756, after the existing Views.
If you visit that clinic on the front end you will see it working (the design is rudimentary).
As an interim solution, so that you can continue to work with the block editor, you could—in place of the problematic Image block—use a shortcode block to insert the wpv-post-featured-image shortcode.
From my classic View you can see that the full shortcode with the attributes required to reference the related employee post (rather than the current intermediate post) is:
[wpv-post-featured-image size="thumbnail" item="@klinik-mitarbeiter.child"]
See https://toolset.com/documentation/programmer-reference/views/views-shortcodes/#wpv-post-featured-image for more details about that shortcode.
Finally, a note on Views and the block editor.
With legacy Views there is a dedicated editor, and you can create a View directly at Toolset > Views.
But when designing a View via the View block the context must be the block editor, which is why you ordinarily create a View by adding a View block to the page where the View will be shown. (The View has to "live" somewhere that uses the block editor.)
Where you might re-use a View in various places it may not make sense to create the View in a specific page, and in that case you might want to create an empty unassigned Content Template (which provides the block-editor context) to host your View, and then wherever you want to insert the View you actually insert its host template.
I think that might help here, as I'm having problems editing Views where they have been added on pages or posts using the Avada editor.
If this were a more generic problem that I could reproduce then I would be escalating these difficulties to the developers, but we are not able to reproduce them on the sandbox site and the problems appear to relate to some specific but hard-to-determine circumstances with your site.