Bedouin

the Fuji 56mm 1.2 works like a dream on X-T4 I used it at 1.2 and it was sharp

Even though I can't offer a solution other than what others have stated here, I will say I bought this lens and used it for it's first official event.  I was photographing three christenings back-to-back in the same church.  The church was extremely well late in afternoon light with large windows down both sides, and skylights running down the center.  Very well lit.  The 56mm on my XT2 would not lock focus.  It was absolutely miserable experience.  I switched to using my 35 1.4, and my 18-55 and breezed through the three events!
So, my experience with the 56 1.2 has not been positive at all and I would never own that lens.  This particular event was on a Sunday, and I returned the lens on Monday morning and have never looked back
Heck, I've used the slow and noisy 60mm 2.4 with better results than the 56...
That was my experience with the 56mm.

I've tried this lens out for about 5 minutes at Fuji and had no issues on my X-T4 
The only quirk was, it refused to eye focus on anyone wearing a mask.  Which was kinda funny when looking at the photo tests and the Fuji guy saying it's a known issue with that lens.
 

Thanks for the update. Sorry to hear of all the trouble. Hope in the end all will get sorted out.

No, I don‘t. Just have used similar lenses with mixed results. In my opinion a lot of experience snd patience ist needed to use them. That doesn‘t mean I think you‘re doing something wrong or have wrong expectations, but some people definitively do (such as me doing the first F1.x shots). I can‘t give an definitive opinion regarding your lens. If you‘re not satisfied with it you should get it checked.

I would stop testing and just send it in. You obviously found something is wrong with your lens, let Fuji check it. Provide them with your test images and description of how you tested.
Henk

You're welcome Bedouin. Fuji paid for transport of the defective lens and for the new lens. I must add that the defective lens had been at the service centre two times without result except "lens tested and is within spec." 
For your test I would use the smallest focus point. Do you have other lenses that you can do the same test with? That would rule-out a camera-based problem.
Maybe something is wrong with the alignment of the lens elements.

Since there is an area if sharpness it seems that the focus point was there. The blurrines might result from the alignment of the object. As I mentioned above, F1.2 gives you a very shallow field of death. Try F5.6 for a start. But maybe you’re right and the lens is defective.

I‘m using different lenses. I‘m not really sure that your photos are out of focus. 

Hi Bedouin, bad luck when a lens behaves like yours. I do not have this lens but had a 35F/2 that behave like your 56mm and was replaced under warranty. If yours is under warranty why not ask your Fuji service center to pay for transport?
Did you use the smallest focus area for your test above?
Henk

What aperture setting did you use? Did you consider that the depth of field is very narrow with an open F1.2 lens?