I checked into the hotel yesterday afternoon and checked out this afternoon. The front desk overcharged me for half a day, but I didn't stay today, just the baggage fee.

In principle, you should pay for half a day's room. Under normal circumstances, you have to check out at noon 12, and some hotels can postpone it until 2 pm. If you don't check out after the deadline, you must pay half a day's room rate.

Even if you don't check in, but you don't check out and take your luggage, no one else can check in.