MWE:
\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{tikzmark}
\usetikzmarklibrary{highlighting}
\begin{document}
\noindent\begin{minipage}{5cm}
The sun was shining on the sea, shining with all its might.
\StartHighlighting[fill=cyan!50]
And this was very odd because it was the middle of the night.
\StopHighlighting
The moon was up there sulkily because she thought the sun had no
business to be there after the day was done.
\StartHighlighting[fill=magenta!50,/tikz/highlighter/left margin=0pt,
/tikz/highlighter/right margin=0pt,
/tikz/highlighter/initial offset=0pt,
/tikz/highlighter/final offset=0pt,
]
‘‘It’s very rude of him,’’ she said, ‘‘to come and spoil the fun.’’
\StopHighlighting
\noindent The sun was shining on the sea, shining with all its
might.
And this was very odd because it was the middle of the night.
\StartHighlighting[fill=yellow!50]
The moon was up there sulkily because she thought the sun had no
business to be there after the day was done\StopHighlighting.
‘‘It’s very rude of him,’’ she said, ‘‘to come and spoil the fun.’’
\end{minipage}
\end{document}
As we see with magenta,
/tikz/highlighter/left margin=0pt,
/tikz/highlighter/right margin=0pt,
/tikz/highlighter/initial offset=0pt,
/tikz/highlighter/final offset=0pt,
is not enough.
By the way, if instead the four lines above, I use/tikz/highlighter/margin=0pt, this gives this error:
Package pgfkeys Error: I do not know the key '/tikz/left margin', to which you passed '0pt', and I am going to ignore it. Perhaps you misspelled it.
Yes, /tikz/highlighter/margin gives an error related to /tikz/left margin, despite the manual speak about the margin key:

MWE:
As we see with magenta,
is not enough.
By the way, if instead the four lines above, I use
/tikz/highlighter/margin=0pt, this gives this error:Yes,
/tikz/highlighter/margingives an error related to/tikz/left margin, despite the manual speak about themarginkey: