so like, the way my pen snaps to the edge of the path in the 1st image, except on the stroke in the 2nd image (which currently it doesnt snap to)

I really dont like how converting strokes to paths (or cropping/combining round paths) will distort the output path, even if to a largely neglegible state. So i thought id try something along the lines of using the "handle to path" snapping with the pen tool to essentially build the shape i desire without having to use path clipping. The problem i have, though, is that this snapping doesnt seem to work with the edges of strokes, which is an issue because i dont know if theres any way to make the sort of shape in the 4th image without it being a stroke.

bear in mind that im saying all this with the assumption that a shape like the 4th image can't be made as a path without using the "stroke to path" tool, or that there isnt any way to circumvent the distortions caused by path conversion/path clipping. But if there are any ways to solve those things, i'm all ears!

(3rd image is my current snapping settings)

If image 4 shows a partially circle an "arc" is a parametric state of the ellipse tool - no conversion needed- if I understand your goal.

what im looking for is a way to have the "handle to path" on the edges of the stroke itself; the path which the stroke comes from doesnt really matter. in your attachment, the "handle to path" goes through the center of the stroke since its, well, snapping to the path, but i need some way to snap around the stroke's edges, not the path.