What’s the optimal approach for KNN (K- Nearest Neighbor)?

Depends on what you want to optimize for. See this paper

https://arxiv.org/abs/1702.08734

And this library that it describes

https://github.com/facebookresearch/faiss

Which is an optimal use of your time as you can install it in a minute with anaconda if you use Python.

In 2D? 3D? <10D? In high-dimensional space?

Binary, continuous, or count vectors, or a mix? Or something more novel?

What's your distance or similarity method?

Is there a bound to your search?

Exact or approximate? If approximate, what counts as good enough?

All of these affect "optimal".