Cloud security loop: New Mac asking for passcode of 'ghost' device

I just got my first Apple product (Macbook Air m5, 15 inch) and I am having insane issues regarding iCloud. I once logged into a university owned iMac about 7 years ago and I had created an Apple account to use it. Now that I have my macbook, when logging in to my account it prompted me to enter the password for that public desktop. I obviously don't have access to the password as that was 7 years ago and I used it only one time just to try it out. When I say that I don't have/remember the password for that desktop, it tells me to try again later. I've had this device for a week and have tried so much to trouble shoot it and it just keeps notifying me that "Some iCloud Data Isn't Syncing" when there shouldn't be data to sync from that public computer. When logging into my Apple account and iCloud.com, the university desktop doesn't even show up on the list of the devices so I can't remove it that way either. I feel like I'm being haunted by this device and I don't know what to do to get it to stop. I'm wanting to get an iPhone soon too and I'm worried that the device will also be haunted by this issue.