Saving money and weight, you could get a used D750. It will use all of your current lenses without an adapter and weigh almost 20 ounces less than your D4. The D780 is newer tech than the D750, also only weighs 29 oz. It is only 4 oz heavier than the mirrorless Z6 & Z7, (which you need an adapter for if you want to use your current lenses.) I like my D750 as it also has a built-in flash, so you never have to fuss with the weight or hassle when it comes time to add some fill. Let us know what you finally end up with; good luck!

The Nikon replacement for the D4 would be the Z9, and that is nearly as heavy. And, if you want to keep your lenses, you have to add the FTZ adapter, which brings the weight up to match.

You could look at the D500; still a good camera for action (although not as good for low light action).

Thanks. I heard Z9 is equally heavy.
I have many lenses. Not that many telescopic. Only Sigma 150-600. This lens is heavy. I am not considering Simi or other equipment simply because I have many lenses, speed lights and other Nikon equipment.
Will look into D500.
You don't mention the lenses, but if you don't have the PF lenses (300mm, 500mm) you should look at those; they are sharp and light and fast enough.

You should also look at Sony for full frame, or Olympus for micro four thirds.

If you would provide a little more detail as to what fast action to which you refer, it might help focus the responses even more.

I have used a Z6 with FTZ adapter quite successfully photographing indoor basketball, volleyball, gymnastics and hockey. I wanted to try the Z6 before really committing to mirrorless so I used the FTZ along with my existing F mount lenses from Nikon, Sigma and Tamron. All worked well.

Don't forget you have the option to rent a camera body and adapter and see how things work for your style of shooting. I have used Lensrentals in the past and been very happy. Two out three times I rented a body I ended up buying one. The third time I saved quite a bit of money when I found out it didn't give me what I thought it might. Keep that in mind as well.