None of them had a dictatorship of the proletariat or worker-owned economy. India and Iraq (and presumably also Mexico) were all dominated by the national bourgeoisie and were just anti-imperialist capitalist states.

The Indian ruling class that collaborated with the British so that the power be handed over to them were mostly wealthy high caste Hindu property and land owners (bourgeoisie). The economic system that followed was agrarian and dirigistic capitalist with meagre social programmes (without which people would have died of starvation since centuries of British rule had robbed communities of food self sufficiency and we relied on central distribution of foodstuffs).

The Indian ruling class was not socialist. So the country was not socialist. India loosely allied with the Societ Union while leading the Non Alignment Movement but that was mostly out of realpolitik needs since Pakistan was getting cozy with the US.