Very much an ‘it depends’ answer as you surmise. But in that situation I would expect ATC to understand the issue and agree a point after which the runway is yours. However, there are academic discussions that can be had about what sterile means - for example, are departures ok whilst your aircraft is on approach, can vehicles cross the runway before you get there, and so on. My personal view would be in the circumstances you describe that I would not allow anything on the runway after you are committed to land but I have no doubt others may hold different views. And I suspect those views may be different at a very busy airport.