If it were me, I'd get the kit with the two Z DX lenses.

First of all, you only get f/3.5 at the 18mm end of the F-mount lens. By the time you zoom to 300mm the max aperture drops to f/6.3. You get the same f/3.5 at the wide end of of the 16-50mm and the same f/6.3 at the telephoto end of the 50-250mm. So there is no advantage what-so-ever, with respect to max aperture.

When it comes to f/16 and f/22, you're correct. The two Z-mount lenses smallest aperture is f/16 while the smallest the 18-300mm can do is f/22. However, this is meaningless. I would never used f/22 on any of these lenses due to diffraction. For that matter, I'd try to avoid f/16. On a 21MP APS-C format camera like the Z50 I would try to keep to f/11 as the smallest aperture I'd use without a lot of concern. A minor exception might be when trying to produce a "sun star", where a really small aperture may be needed. But not all lenses are good at producing sun stars, due to the design of their aperture. This would be something to investigate, if you think sun stars might be important to you at some point. ("Sun star" is a bit of a simplification... similar stars can be created around any strong light source, such as street lights in a cityscape at night.)

I am simply not a fan of "do everything" or "all in one" zooms. They may be convenient (minimal or no lens changes), but usually compromise in some ways.... lower image quality or other things. An 18-300mm is pretty extreme... a 16.66X zoom (divide 300 by 18). In contrast, the Z lenses are roughly 3X and 5X. Much less extreme and potentially better image quality. I can't prove better image quality either way because I don't have these lenses or know of a website where they have been thoroughly tested and can be compared. At a site where I found test shots done with the 18-300mm, I wasn't impressed with the IQ of the lens at the wide end, where it was low contrast and showed a lot of chromatic aberration. Most CA disappeared once it was zoomed to the telephoto range, but contrast appeared to remain low.

Unfortunately there is no test of the much newer Z-lenses at that site, for comparison. Maybe someone here has experience with all three lenses and can tell us more.

There's also size to consider. While the 18-300mm is reasonably compact for the range it covers and not particularly heavy, the camera + lens "package" with the 16-50mm mounted is quite a bit smaller. The 50-250mm is larger, of course, but not quite as large as the 18-300mm. Combined weight of the two Z lenses is very close to the weight of the 18-300mm, too. By the time you add an adapter to the F-mount lens, it will be bigger and weigh a little more. To be fair, it's a relatively minor size and weight penalty.

16mm wide is significantly different from 18mm wide, while 250mm telephoto really isn't all that different from 300mm. There is no wide Z DX lens yet, so those 2 additional mm of width might be quite useful for the time being (though a Nikkor AF-P 10-20mm might be adapted).

Not to mention, it would cost more to buy the Z50 body, an adapter and the 18-300mm. At a minimum that will cost $1600 (w/cheaper, 3rd party F-to-Z adapter like Viltrox... the Nikon brand adapter bought separate goes for 5X as much).

In comparison, the Z50 + 16-50mm + 50-250mm lens costs about $1250.

Anyway, I know what I'd do. I would get the kit including the Z50 and the two Z DX lenses.