I feel silly, but since I just got the game at beta 8.1 about a week ago, I cannot figure out how to update it to 9. I do not see a link or something similar within the list of files/attachments, so I am at a loss. Forgive me for the ignorance.
Viewing post in [Update] Beta 9: Friendship, romance, and blackmail comments
You can download the app that can update the game automatically: https://itch.io/app
Or you can just delete the game folder and download the new version, there should be a "Download" button at the top of this page https://sadambober.itch.io/idol-manager
Your save files are in a different folder, so you should be safe