Trying to tighten a saddle clamp but nothing seems to give
It may be a silly question from my side: Did you loosen the bolt on the seatpost clamp (the one above the blue tape)?
The saddle clamp isn't screwed in but either shrunk-fit or glued in place. So your seatpost is toast. Removing a stuck post is a classic problem. It can be very hard, if the post hasn't been taken out for a long time and put back with a liberal coat of grease, anti-seize paste or carbon compound if either post or tube, or both are made of carbon.
To remove the post, try first with penetrating oil and letting it soak for plenty of time. If you can rely on a mate to hold the frame grip the post with a water pump wrench. Be careful though not to damage your frame.
On YouTube in bicycle dedicated channels you may find several more methods to proceed as it is quite a common problem.