Does anyone know how to do this in Vectr (or is Vectr just not up to the task)?
I've never heard of Vectr before, but looking at it for a few moments, and using the online version, there does not appear to be any method to alter end caps of strokes on paths, or alter shapes in any sort of custom manner. It looks, exceptionally rudimentary in it's editing capabilities, generally only allowing basic predefined shapes and standard bezier paths. Checking their help section, there's no reference to rounding anywhere or end caps.
You may be better off exploring something like InkScape (which is free). Inkscape offers much more editing capabilities.