how to make the end of a curve round? (like pictured in the image? could it end somehow on a 'semisphere?)
I agree with @Vagabonk's comment, that's a neat method, but it does depend on Catmull-Clark's approximation of a square subdividing as a circle, which isn't perfect, and a level of subdivision you might not want.
Here's a GN group which will modify a given curve to round-capped bevel of itself, with set radius, U & V resolutions:
Improvements could include UV mapping in continuity with the caps.. that might be easier in Blender 3.3.