There is nothing strange, actually. If I try \showhyphens{StackExchange} the answer is
Stack-Ex-change
Those are the only points TeX is willing to break a line at. In your first attempt, breaking after x would produce a line where interword spaces are stretched a lot. This doesn't happen in the other two cases. Here's a slightly modified version of your code (I don't own Calibri Light, but adding one millimeter to \textwidth faithfully reproduces your issue) where the effect of breaking the line after x.
\documentclass[11pt, oneside, a4paper]{article}
\usepackage{fontspec}
\usepackage[normalem]{ulem}
\usepackage{hyperref}
\setmainfont{Calibri}
\addtolength{\textwidth}{0.1cm}
\begin{document}
\textbf{\underline{This is overfull:}}
Code was written with the help of
\href{https://tex.stackexchange.com}{\uline{tex.stackexchange.com}}
(all hail \emph{StackExchange}). There, many friendly people from the community
are helping each other out on all sorts of computer-related problems.
\textbf{\underline{This is how it would be:}}
Code was written with the help of
\href{https://tex.stackexchange.com}{\uline{tex.stackexchange.com}}
(all hail \emph{StackEx-\linebreak change}). There, many friendly people from the community
are helping each other out on all sorts of computer-related problems.
\textbf{\underline{But this is fine:}}
Code was written with the help of
\href{https://tex.stackexchange.com}{\uline{tex.stackexchange.com}}
(all hail \emph{TexStackExchange}). There, many friendly people from the community
are helping each other out on all sorts of computer-related problems.
\textbf{\underline{This works, too:}}
This document was written with the help of
\href{https://tex.stackexchange.com}{\uline{tex.stackexchange.com}}
(all hail \emph{StackExchange}). There, many friendly people from the community
are helping each other out on all sorts of computer-related problems.
\end{document}

Instead of producing a very bad line, TeX prefers to output an overfull one, warning you it did, so you can examine the offending paragraph and reword it
to make it fit.
However, adding microtype can be very helpful.
\documentclass[11pt, oneside, a4paper]{article}
\usepackage{fontspec}
\usepackage[normalem]{ulem}
\usepackage{microtype}
\usepackage{hyperref}
\setmainfont{Calibri}
\addtolength{\textwidth}{0.1cm}
\begin{document}
\textbf{\underline{This is acceptable:}}
Code was written with the help of
\href{https://tex.stackexchange.com}{\uline{tex.stackexchange.com}}
(all hail \emph{StackExchange}). There, many friendly people from the community
are helping each other out on all sorts of computer-related problems.
\microtypesetup{protrusion=false,expansion=false}
\textbf{\underline{This is how it would be without microtype:}}
Code was written with the help of
\href{https://tex.stackexchange.com}{\uline{tex.stackexchange.com}}
(all hail \emph{StackEx-\linebreak change}). There, many friendly people from the community
are helping each other out on all sorts of computer-related problems.
\end{document}

Stack-Ex-change. In the first case, choosing either hyphenation point would produce a paragraph with badness exceeding the tolerance, so TeX produces an imperfect one for you to fix it. – egreg Feb 21 '20 at 09:03\usepackage{microtype}, it should do its best to 'fix' such lines. (btw you don't need to loadfontencwhen you're usingfontspec) – TivV Feb 21 '20 at 09:08\usepackage{microtype}does a better job, but does not fix it entirely (the full stop still overflows). I also want to use\usepackge[none]{hyphenate}to prevent hyphenation and in that casemicrotypemakes it even worse. @egreg Not sure if I understand you point, what is your suggestion to fix this? – s6hebern Feb 21 '20 at 09:16\sloppyto allow white space to stretch much more. Constraining white space not to stretch and specifying justified paragraphs and disabling hyphenation is setting unachievable constraints. – David Carlisle Feb 21 '20 at 09:18