In order to monitor the Guest User accoun in the Debug Log (as shown below)

You need to use the Site Name of your Site in the User Search dialog when setting up the debug log (note NOT the Site Label).

You won’t be able to search for the user using the lookup or use its ‘full name’ which if you notice in the screenshot above is actually ‘Site Guest User, Project Application’

The red box indicates the Site Name as found in the Site Details screen