The database is stored on the client in different places:
- Windows: / Users / {user} / AppData / Apple Computer / Safari / Databases
- Safari: ~ / Library / Safari / Databases
There is a main database file in this folder that points to your database in the corresponding subfolder. You can see the size of the database in Explorer / Finder. However, I find that the size of the database is platform dependent (and the size of the database varies greatly between Safari and Chrome).
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