Hello vatar_je42,
Welcome to Apple Support Communities.
We understand that when you wake or restart your Mac that the login screen shows on the projector rather than the Mac or display. We are happy to help.
Has the login screen always showed on the projector or has it displayed on the Mac or external display? when did you first notice this happening? Have you made any recent changes to your Mac? These answers will help us the isolate the cause.
We recommend doing some isolating troubleshooting steps—test in safe mode and new user account.
Here’s ho to start in safe mode to test: How to use safe mode on your Mac - Apple Support
"Apple silicon
- Shut down your Mac.
- Turn on your Mac and continue to press and hold the power button until you see the startup options window.
- Select your startup disk, then press and hold the Shift key while clicking “Continue in Safe Mode.”
- Log in to your Mac. You might be asked to log in again."
Here’s how to test in a new user account: Change Users & Groups settings on Mac - Apple Support
"Create a new user or group.
Click the New Account pop-up menu (you may be asked to enter your password), then choose a type of account.
- Administrator: An administrator can add and manage other users, install apps, and change settings. The new user you create when you first set up your Mac is an administrator. Your Mac can have multiple administrators. You can create new ones, and convert standard users to administrators. Don’t set up automatic login for an administrator. If you do, someone could simply restart your Mac and gain access with administrator privileges. To keep your Mac secure, don’t share administrator names and passwords.
- Standard: Standard users are set up by an administrator. Standard users can install apps and change their own settings, but can’t add other users or change other users’ settings.
- Sharing Only: Sharing-only users can access shared files remotely, but can’t log in to the computer or change settings. To give the user permission to access your shared files or screen, you may need to change options in File Sharing, Screen Sharing, or Remote Management settings. See Set up file sharing and Share the screen of another Mac.
- Group: Groups allow multiple users to have the same access privileges. You control a group’s access to your shared folders by setting access permissions in the File Sharing options in Sharing settings.
See Add a user or group."
Let us know if you have further questions.
Take care.
