I believe this is the one the media outlets are saying is a fake. Doesn't match the length of the one described by law enforcement and doesn't contain phrases quoted by major media outlets.

This one has been confirmed by some major media outlets as being genuine and matches the description by law enforcement and the select quotes published by established media:

https://www.kenklippenstein.com/p/luigis-manifesto

There could of course be other writings by the suspect, and this could be one, but it's definitely not confirmed.

Seems suspicious. If you look at Archive.org, the site was only crawled on December 9, 2024, and not before.

Yes, I did a search and could not independently confirm. Interesting read, but no idea if it’s real.