Thank you for joining the thread, @stello21.
Allow me to share some insights about completed projects in QuickBooks Online (QBO).
You have to manually mark the project as completed from the Projects window so it won't show up under the Choose a customer or project drop-down on your Timesheet.
When creating timesheets, the project will never show up on the drop-down list.
If the problem continues, log out and log back into your QBO account.
Let me know if you have any other questions. I'm always here to help. Have a good day!