Also, I am deeply suspicious if they can properly support searching with Ctrl+F...

And yes, browsers should be just able to render the diffs, if the styling is somewhat minimal and there is no JS: I have a 6.3-MiB large HTML file with complete transcript of a certain TV series, formatted like

    <dd><b>Character #1</b>: Well, that was interesting all right.</dd>
    <dd><b>Character #2</b>: [sigh]</dd></dl>
    <dl><dd><b>Character #1</b>: Lemme help you.</dd>
    <dd><b>Character #3</b>: Yeehaw!</dd>
    <dd>[thump]</dd>

(the </dl><dl> produces a small paragraph break, to indicate scene transitions), and it scrolls and searches just fine.