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I have installed System Shock 2 GOG version, with all the mods recommended in the sticky post, exactly as directed.

This may be a minor issue or a misunderstanding on my part. The sticky post says the "cutscene rebirth" mod improves the look of the intro animation. And yet I have seen the intro both before and after applying the mod, with max resolution and minimum resolution, and the cutscene shows no improvement in quality.

Looking closer at the Cutscene Rebirth file, and playing it outside the game, it's a different file... not part of the introduction. Am I missing something here?
Well... The simplest thing for you to do is simply to watch the remastered intro outside of the game and go play the game itself. Really, it's no big deal, and definitely not quite worth putting an effort into solving (good as a bug report tho)
When they say 'intro animation' it's a little bit of a misnomer. There are 3 main cutscenes (not counting the short shuttle launch videos) which are named cs1, cs2, and cs3.

cs1 is what's played when you press the "Intro" button at the main menu and also when you initially start a new game.

cs3 is the end game cutscene.

cs2 is the cutscene which is replaced in the 'Cutscene Rebirth' mod. This scene does not start until after you have completed the training portion at the start of a new game. There's a noticeable difference for the cutscene, you'll just need to play a little more to see it in game.