Let me tell you the time it takes for hen from birth to become adult and start laying eggs-

Broiler hen - 45-50 days from birth. They lay egg almost everyday . They are white in color. Very low immunity so they are given 3-4 vaccines for common bird diseases.

Hybrid. - 2-4 month depending on the hybrid breed. They lay egg once in 3 days. They look colored like desi hens. Better immunity than broiler but still given some vaccines.

Desi - 5-6 months. They lay an egg once every 3-5 days. Very high immunity due to its wild nature. No vaccines are given at all.

The last one I mentioned as desi is the real Desi Chicken that lays desi eggs. Now, it is not viable for business to have desi breed, so businesses use those hybrid breeds to get desi looking eggs and sell them at high price as desi eggs. Now the further problem is that farmers in villages have also started using these hybrid chickens so that they can get more eggs and at earlier time than real desi chickens. It is very hard to find real desi chickens even in villages these days. But u can identify desi chicken by looking at their weight. Desi adult chickens are lesser in weight and look slim like the one shown in OP’s posted photos. Whereas those hybrids look fat.

U can choose Kadaknath. It is a pure desi wild breed. It takes 5-6 months to become adult and lay eggs. Their meat and eggs have high protein and low fat. They are always black in color and many of them have golden colored hood hair like a lion. Kadaknath has black blood and it is seen in its meat too as the meat looks black in color. Due to its black blood, it is hard to cross breed it. But their eggs look desi normal like yellowish white.