What sharpening actually does
Sharpening does not recover detail. It cannot — the detail is either in the file or it is not, and no filter can invent what the lens did not resolve. What it does is increase contrast along the edges that are already there, which the eye reads as sharper.
The classic technique is the unsharp mask, named after the darkroom process it copies. A blurred copy is subtracted from the original to isolate the edges, and that difference is added back amplified. Radius sets how blurred that copy is, which decides the size of the detail affected; amount sets how much of the difference is added back.
Because it is contrast amplification, it cannot distinguish an edge you want from grain you do not. That is not a flaw in a particular implementation — it is what the operation is — and it is why the threshold matters so much.