The "only x rooms left" notices are also BS, even if they're dealing with the big hotel chains. And even when dealing with those, there are frequent inventory discrepancies due to how long it takes for the systems to communicate with each other, so best option in my opinion is to always use the official hotel channels. It's also cheaper if you're a member of their frequent guest programs, which is free.

You as a hotel operator can use booking.com's software to manage your entire inventory. Thus they know how many rooms are available. This is common in small guesthouses and hotels - but obviously not in larger hotel chains.