Made so I can know all of the restrictions so please add on to this list and I will update it with comments.
Quick list of things from someone who has played the game on what can be played offline:
Restrictions:
Customization will not be saved offline.
Nothing can be unlocked. So after beating Story Mode you will be greeted with the credits... And thrown to the title screen without unlocking Frost or anything.
Koins generated (For Krypt) are reverted to 0.
Entirely disabled:
Towers of Time
Krypt
Online
AI Battle
Anything that requires saving or unlocking things excluding Tower endings and Story Mode progress.
Quick list of things from someone who has played the game on what can be played offline:
Restrictions:
Customization will not be saved offline.
Nothing can be unlocked. So after beating Story Mode you will be greeted with the credits... And thrown to the title screen without unlocking Frost or anything.
Koins generated (For Krypt) are reverted to 0.
Entirely disabled:
Towers of Time
Krypt
Online
AI Battle
Anything that requires saving or unlocking things excluding Tower endings and Story Mode progress.