Variables being overridden to initial values.

[buran]

because they have local scope inside the function. you need to declare them as global, using global keyword if you want to change the global name.
Note, if you don't assign to a name inside the function, it will use the global one, without need to declare it global
e.g.

def SET_MOST_RECENT_BACKUP():
    print("Step 3...")
    global MOST_RECENT_BACKUP
    MOST_RECENT_BACKUP = CURRENT_LIST_OF_BACKUPS[-1]
    print(MOST_RECENT_BACKUP)

CURRENT_LIST_OF_BACKUPS is a list and lists are mutable, that's why it "works" for it.

Note that using globals is generally considered bad, pass arguments to functions and return from functions.
Also, using ALL_CAPS for function and names is not consistent with PEP8 recommendations.