Briggs & Stratton Classic not running well. Carburetor broken?

Hello,
 
I have a mower that runs pretty poorly in that is runs and stutters. I can see puffs of black smoke from the exhaust every time it stutters. The spark plug goes black with soot, indicating rich running.
 
I have serviced that carburetor with new diaphragm, gasket and cleaned it all with carb cleaner and compressed air.
Twice actually and I also removed the main jet for cleaning.
 
None of made any difference and it runs exactly like before.
 
When looking into the carb, onto the main jet, I can see petrol drops coming out there and flying baout and ever time I see a big drop coming, the splutter follows.
  
Here is a video of this:
(Sorry, it was hard to hold the torch and the camera at the same time with precision)
 
EDIT: This forum does not seem to allow links (perhaps because I am still new). 
Please paste the text below into your browser to get to the video clip.
 
youtube.com/shorts/8uKIvhzcnhk
 
 
I am not not sure what next to do. The carb is clean and apart from some wear in the throttle shaft, I can't find anything wrong with it.
 
Do I need a new carburetor or is this problem caused by something else in the engine perhaps?
 
Best regards
Bernt
 
 

Also, check the tightness of the THREE HEAD BOLTS closest to the exhaust.
They tend to loosen over time.  
 
It almost sounds like you have a head gasket leaking (loose head bolts)?
Spray some soapy water around the head to cylinder and look for any  bubbles
(before the engine gets too hot).  
 
.

Tks for the update.  
 
Try a new (known as good) spark plug and check for good spark
with the plug grounded to the head.
 
As I noted earlier, it sounds like more than a rich running condition.
 
A bad coil, spark plug, may not work 100% of the time.  Excess fuel 
can build up / load up W/O spark 100% of the time....
 
You may also want to check the flywheel key, it's not sheared and 
that the coil is installed correctly (if machine is new to you). 
 
.