I'm speaking of the normal DOM representation of the HTML in the page. A server-side highlighter generates HTML with css classes or styling attached that gets turned into a DOM by the browser. A JS-based highlighter edits the DOM by adding css classes or attaching styling. The in-browser representation of the end result, which a browser extension likely works with, can be the same, and how it looks like exactly is more important for their functionality than if the server or JS did it.
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I'm speaking of the normal DOM representation of the HTML in the page. A server-side highlighter generates HTML with css classes or styling attached that gets turned into a DOM by the browser. A JS-based highlighter edits the DOM by adding css classes or attaching styling. The in-browser representation of the end result, which a browser extension likely works with, can be the same, and how it looks like exactly is more important for their functionality than if the server or JS did it.