Not who you replied to, but it's consistent with basically other source I can find. I'm inclined to believe that the root for year is indeed different, based on the suggested cognates in other languages.
https://www.merriam-webster.com/dictionary/annual
https://www.merriam-webster.com/dictionary/anus
https://www.etymonline.com/word/annual
https://www.etymonline.com/word/anus