Several yrs. ago there was talk of commercial jets using propfans. I recall seeing pics of them. Ultra high bypass.
For one reason or another the concept hasn’t taken off.
Turboprops use reductions gears to drive the propeller so the blades don't exceed the speed of sound. IIRC, the propjet's blades run directly so there is a continuous sonic boom as the blades break the sound barrier. It would be quite a feat to pass Federal noise regs, but the Indian Navy doesn't have to, I suppose.
No one had ever designed a propeller that was efficient above the speed of sound. Various airfoil shapes were to be tested, but I don't know if they found the right ones.
The blades ran unshielded, on the outside of the engine (like a jet engine with the cowling off, and the turbine blades running at mach speed naked to the world). A catastrophic failure could be deadly to anything nearby.
Often referred to as Unducted Fans, or UDFs.
One reason why they have yet to be adopted: Extremely noisy, and noise abatement laws have gotten much stiffer around airports as suburbia encroaches on the world's airport locations.
Another reason why they have yet to be adopted: No way to control a lost fan blade from potentially penetrating the cabin. Since the 1990s, all commercial jet engines must be able to contain lost blades for certification.
Neither of these problems are insurmountable, nor is the additional problem of mechanical complexity required for the UDF's additional gear reduction and fan blade pitch control. One proposal is to put the engines at the back of the airplane, and above the fuselage so that the horizontal tail blocks noise from reaching the ground.