To gear snobs all lenses are inferior except the most expensive one they own.
To actual photographers no modern lens is inferior, it's just that some lenses are less not-inferior than some other lenses. But really good photos can be taken with any of them in the hands of a skilled photographer who understands their limitations and works just within the bounds of those limitations. And all lenses, even the most expensive ones, have limitations of some kind.
Pretty much every zoom lens introduced in the past 15 years for interchangeable lens cameras is better than 95% of what was available only 25-30 years ago when "kit" zoom lenses first started appearing on the scene instead of 40mm or 50mm primes being the lenses most often included with a new camera body. Other than a few really cheap lenses that have been around since way back then and are still being sold new, none of which are primary "kit" lenses, current lenses are pretty much all better than 100% of zoom lenses available for 135 format (35mm) cameras back then. That's when "kit lenses" got the reputation as being poor lenses.
Sure, there are always more expensive lenses than the cheaper ones on the market at any given time. In general, the more you're willing to spend on a lens the better it will be, at least for the use case for which it was designed. Just don't expect a great macro lens to also be a great portrait lens, and vice-versa. They're built for two different purposes. More expensive lenses also tend, at times, to be more specialized lenses that are optimized to do one particular thing very well. Kit lenses, on the other hand, are designed to do many things as well as is possible at a certain price point. But just because one $700-800 lens comes in a "kit" and another $700-800 lens does not come in any kits does not mean the latter is necessarily better than the former.
Having said all of that: The main problem with your D5600 probably isn't actually the D5600. It's probably the 150-600mm lens, most of which tend to be relatively slow to autofocus and perform worst optically at their longest focal length which is the focal length everyone buys them to use. I'd venture to say that any Nikon normal zoom for APS-C in the 18-55mm range made in the past ten years is a better lens than the 150-600mm you're using (regardless of which version of Tamron or Sigma it is) with your D5600. So you're doing a bit of an apples to oranges comparison complaining about a 150-600mm telephoto zoom and then wondering how various 16-80mm lenses stack up against each other.
If you're bound and determined to get a new body then the two choices you have suggested are both pretty good cameras, but each has advantages over the other. The mirrorless Fuji will almost certain have a better AF system than the Pentax DSLR. The Pentax DSLR, though, will be more environmentally resistant to water and dust than the Fuji will. So which is more important to you? Only you can answer that.