Yeah, they are deeper more than high. But not all are exactly the same sizes. But yeah, I’ve put my small Very Bradley bag in the free lockers, with my ball cap, not stuffed at all. But know my bag only has phone, small wallet, phone charger with wire, sunglasses and sometimes my car keys. So it’s not that big.
Yes, bottles need to be laid sideways, and wands need creative placement to get it inside the locker, with its box, even harder to get it in flat.