I followed this course a long time ago (April 2021) and at that time it was created using cocoapods to install the Firebase frameworks. SPM, as you have discovered, is now the preferred method since it is simpler once you get the hang of it.
For this course you only needed to select these two framework options from the Package Manager window
FirebaseFirestore
FirestoreFirestoreSwift
I have made some changes to your project so that it now should work. There is no need to have an AppDelegate instance in the project as a means of initialising Firebase. The init method that was described in the course is perfectly sufficient to achieve that task.
Instead of using import FirebaseCore all you needed was import Firebase
Here is a link to your updated code:
I moved the function you had created - makeReservation - to ContentView and created a Button to call that function.
Each time the course covers a particular aspect of creating a record, it’s easier to create a new function to do that as a means of keeping a record of what you did previously. It also gets you used to writing similar code which helps you remember what to do. When you want to run that new function, just change the code in the button action to call it.