How feasible it is to use the aperture radar tech to make an imaging seeker for surface-to-air defence systems? Some sort of IIR seeker that operates on the X-band radar section of EM spectrum instead of IR section?
There are lots of surface-to-air missile systems that use seekers in X, Ka & Ku-bands. There are even AESA-based seekers in those frequencies these days.
Here are some models made in India:
...I'm sure Turkey makes them as well.
As of SAR, its more a definition of a radar system (inclusive of the computer & software behind it) that's capable of a certain technique
rather than a type of radar in of itself. A synthetic aperture is where you collate the inputs of a moving radar over time to generate a "bigger" or "higher resolution" picture than what the radar's own aperture size is otherwise capable of. Hence 'synthetic' aperture.
The SAR technique is more useful to generate high-resolution imagery of a very cluttered environment like the ground (or even sea surface, all the waves create lot of clutter) as you need the extra clarity to identify potential targets. But when dealing with airborne targets, there isn't so much clutter - the background is just the sky.
So SAR isn't really useful for anti-aircraft applications.