A session is not an appointment with extra fields
Most booking software was built for a person and a diary. A timed session with a fixed capacity is a different thing, and every workaround you have ever built exists because something was pretending otherwise.
Timed, fixed-capacity sessions, natively
A session has a start, a length, a resource and a number of places. It sells down to zero and then it is gone. That is the object the whole engine is built on, rather than a generic appointment with a capacity field bolted to the side.
It means the awkward cases are ordinary. Two people booking the same eleven o'clock separately. A party of nine that arrives as a six and a three. A session that must not be split at all. None of these need a note in the booking or a rule your staff carry in their heads.
Buyout, buffers and tables that push together
Private buyout is a native model, not a discount code with a warning attached. Sell the session whole, close it to everyone else, and price it as the thing it is.
Buffers sit between sessions and belong to the resource, so a reset that takes fifteen minutes takes fifteen minutes on the public widget too. Nobody is protecting the turnaround by quietly not publishing an eleven o'clock.
Combinable resources handle the tables that push together. Two fours become an eight, the eight disappears from availability when either four is sold, and the arithmetic is the system's problem rather than a duty manager's.
A hold while the card is being entered
When a customer reaches checkout the places are held. For the length of that hold the slot cannot be sold underneath them, and when the hold expires the places return to sale automatically. No ghost bookings, no manual sweep of half-finished carts.
Under real concurrency, holds are not enough on their own, so the write path locks the session before it decides anything. Two requests for the last two places on a Saturday are serialised: one is told yes, the other is told no, and the second one is told before any money moves.
Overselling a fixed-capacity session is not a rare edge case in this category. It is Saturday at seven. It is treated as a correctness problem, not a support problem.