It's the standard word for a set of four connected works: https://en.wiktionary.org/wiki/tetralogy
That entry mentions "quadrilogy" as a non-standard synonym, while it's not even in Merriam-Webster, the American Heritage Dictionary, or the Online Etymology Dictionary.
Below are the entries for "tetralogy" but if you search for "quadrilogy" they all just say it isn't found: M-W: https://www.merriam-webster.com/dictionary/tetralogy AHD: https://www.ahdictionary.com/word/search.html?q=tetralogy EtymOnline: https://www.etymonline.com/word/tetralogy
The larger point is that the prefix and suffix for each word for a set of connected works come respectively from the Greek number-word and the Greek "logos"; this leads to dilogy, trilogy, tetralogy, pentalogy, and even less-common words (same as the -athlon words), while "quadri-" comes from Latin.
In case you're thinking "Why don't you complain about the other 'quadrilogy' categories on this site?", the only other one I've seen so far came from the Shantae community and I thought that was a one-off mistake.
(BTW, I'm not complaining about the "-athlon" categories here, and FWIW, renaming it to "tetrathlon" would also be standard, but that word is much less common than "tetralogy".)