What do 'you' think you mean by 'sharpness'?
Its a mush over used and seldom defined and even less well understood concept.
The camera focuses, and uses a red dot to arbitrarily guess on a subject in the scene to focus on. Whats in or out of focus, or 'acceptable focus' will be a distance fore and aft of that guess point, proportional to a) the focus distance that the red-dot guessed, and the aperture that the elektrikery probably selected in the settings for the exposure that were used.... what you percieve as 'sharpness' in the resultant picture, is then a combination of factors in which the lens and the camera play but tiny p[art, and more the contrast between elements in your scene are differentiated....
Ie the 'sharpness' of a photo has almost noting top do with the quality of your lens... it has an awful lot to do with the subject you point it at, the lighting and the composition, then an awful lot more to do with how you use the camera, not even what camera you are using.
I have the D32oo and have had that the best part of a decde. It is more then good enough for me for the most partr, and so is its 'kit' 18-55 lens.
When daughter started her GCSE photo course, I bought her a 2nd hand D31oo, and a 2nd hand AS-D 35DX as her only lens... after an incident in the bathroom with baloons full of water being burst inches away from my camera and its delicate electronics......
I have to say that the AF-S 35DX is a crravking lens, especially for the money.. B~U~T, on it's own it will NOT make your shots any better, let alone 'sharper', even if you have a handle on what 'sharpness' may be or what controls it... YOU however might.
And first suggestion is to get off 'auto' and if worried about your focus, do it yourself,. not leave it to a red-dot.... and be aware of the Depth of Field, and how aperture setting effects that, which may beg getting of auto exposure too..... but more still, being aware how much is down to the subject and lighting and comporition, NOT the cemera or its lens or its settings....
The AF-S 35 'sounds' like a panacea, but believe me, other than the novelty of its wide f1.8 aperture offering razor thin DoF, beyond that it's NOT actually got a lot going for it that the kit 18-55 hasn't.
Going 'primes' is fun, I will say, and I bought an M42 adaptor to use the ;legacy lenses from my M42 film camera with the D32oo. They don't auto focus, and on my D32oo the camera cant even 'meter' with them, so I have to go manual everything and use the thing with less automation than even the old M42 Sigma MK1 the lenses are native too! These old legacy lenses, though are 'cheap' and second hand value of the entire bag full, is probably no more than I paid for Daughter's AF-S 35.... but entire experiment taght me that they were best employed on the M42 Sigma film camera they were native to, and Daughter ultimately got herself an old Nikon FE (I think) film camera to use legacy lenses on.....
Many of these old film only era, legacy lenses, have fantastic resolving properties and offer amazing resolution, as might be perceived as 'sharpness' if that is really what you are after... but it is mostly delivered by old legacy film cameras that demand that YOU do the focusing, and make the settings and use the DoF scale, and pay more attention to your subject, the lighting, framing and composition... it's not something that you 'buy with a different bit of kit.
Which begs suggestions; first that the kit 18-55 is probably good enough, next, you will likely find more difference just going manual focus, and outstanding the settings better, than you will a different lens... and for what you 'say' you want to achieve, chasing that will either throw up a lot of alternatives like film/legacy lenses, and/or take you down a route confirming its the kit in your mitt and GAS rather than the know-how in your head, that matters.
Your call...
That Nikkor AF-S35 remains a cracking and gt value lens though, b~u~t, I'm sanguine, it or anything else is the answer to your preyers.... though you might convince yourself it is