This depends on the missile being used. 9M96E/E2 are the high-maneuvering ones used to shoot down UAV's which have ranges of upto 40/120 km. Multiple 9M96 missiles can be carried per launcher container, making them more far more compact with operational efficiency.
You are right that you wouldn't use this against a basic "quadcopter" drone as it is still too expensive, but Ukraine does indeed have far more sophisticated, speedy/evasive "strategic" drones. They are the undisputed world-leader in drone warfare. Many times the Russians have no choice.
All of the layered Russian air defenses shooting down Ukrainian drone swarms do mention the S-400, but unfortunately they don't give exact target count to each system, so it is difficult to correlate numbers.
I'm talking about Ukrainian shahed-equivalents here.
9M96E/E2 can be used to shoot down shahed-like UAVs, but it's not something you'd generally want to do. They don't exist in sufficient numbers and are far better suited for shooting down missiles. It's something you'd do as a last resort, when necessary. Not something you'd do to shoot down thousands of drones.
The question is not whether or not the S-400 is capable of doing that, of course it is. It's not going to be very good at it, but if someone was willing to waste absurd amounts of money by using the wrong equipment they could certainly reach numbers like that.
Russia isn't stupid, they're not using the S-400 to shoot down thousands of drones. They have equipment better suited for that purpose. Russia does not currently, and will likely never have sufficient numbers of S-400 interceptors to routinely intercept cheap little drones with them.