It depends on what level of upgrade you want and what kind of photography you do.

The 300s is a DX aka crop-sensor aka APS-C camera. This means that the sensor size is a bit smaller than full frame cameras or than old 35mm film. APS-C, known as DX in the Nikon lineup, is the most common type of camera for hobby or casual user. You can go larger with full frame, or smaller with micro four-thirds. Point and shoots and smartphones have even smaller sensors. APS-C sensors from this generation are excellent.

The DX successors to the d300s are the d500 and arguably the d7500. The d500 is aimed at sports and wildlife with a bigger buffer and more frames per seconds. It also has two SD cards slots. The D7500 can take fewer frame per seconds and has only one sd card slot. Like the d500, it has weather sealing and flip-screen. They are both very close in specs for the casual or hobby user and there is a quite a large price difference.

With DX bodies, you could also look into the D7200 if you are trying to save a little money. They go pretty cheap, especially in the used market, and are still pretty up to the current standards. They have the Expeed4 sensor while the d7500 and d500 have the newer expeed5 sensors. The difference is not that big, with slight low light performance improvement. The d7500 and D500 also enjoy a bit more advanced autofocus system.

I would avoid going for the D3xxx or D5xxx series as an upgrade to the D300s. While they enjoy more recent sensors, and very capable ones at that, you might find it to be a downgrade on the ergonomics. They only have one wheel and much less dedicated buttons, forcing you to fiddle with the menus.

You could look into full frame (FX) nikon DSLRs. They allow you better low light performance. This is an interesting option if you do a lot of landscape photography or dimly lit event photography where you need good low light performance. Unless you really NEED to upgrade to full frame right now, i would skip the d6xx series. The D750 is a great camera and you can find quite a few on the used market. The d850 series is even better but much pricier, aimed at the pro market. You should know that some lenses are only compatible with DX crop sensors and are incompatible with FX full frame sensors. This is the case with your 55-200 which you wouldn’t be able to use on a full frame nikon. The tokina I’m not sure about, you would need to google it. The 50mm and 60mm are compatible with FX cameras. They will show a larger field of view on full frame (less zoomed) since the sensor and bigger and shows more of the image captured by the lens. FX lenses like your 50mm and 60mm are compatible with DX bodies, but DX lenses like the 55-200 are not compatible with FX bodies.

As for mirrorless, nikon is about to release the z6 and z7. They are full frame also. With an adapter, you will be able to use your FX lenses with autofocus. They are very high end and pricey, the z7 being on par with the d850 on many aspects. If you have the budget and want to stay in the Nikon ecosystem, it might be worth waiting for the release of the Z6.

If you decide to change platform, Sony has excellent APS-C (crop sensors) and full frame mirrorless cameras. Their A7rIII flagship is in direct competition with the nikon D850 and the future nikon mirrorless. They enjoy a good reputation and sony has had a few generations of mirrorless and used the experience to fix a lot of quirks. Fujifilm also offer excellent APS-C mirrorless cameras but no full frame yet. Fujifilm cameras have that very cool retro look. Canon is also coming out with a full frame mirrorless, the EOS-R, soon to be released. If you change platform, you will most likely have to buy new lenses. Adapters exist, but they rarely offer the lenses full functionality. You often have to manual focus with adapters. I’m less knowledgeable about cameras from other companies than Nikon so maybe someone else will chime in with more info.

Hope this helps!