Community user @Jack19 authored this User Tip for using an external drive as a startup drive on Mac. It says SSD, but the steps also apply for using an external HDD as well.
Use an external SSD as your startup disk … - Apple Community
Have you unintentionally started the Mac in Target Disk mode by holding down the T key? Power off the computer by pressing the power button until the computer shuts down.
If you are trying to restart from a properly configured external drive, one correct process is to press and hold the Option key when you power up the computer.