I’m afraid this answer isn’t useful.
Now, to be upfront, I don’t know much about Kerala, never having been there and is not being a common topic in my readings. That said, I am perfectly happy to accept that everything you say is true. It’s also largely irrelevant, and that’s no insult.
Because Kerala isn’t Communist. It has a Communist party, no doubt, but it’s not Communist. It is, in fact, only moderately Socialist. It;s possible they’ve gone and redefined COmmunism to suit themselves, but it meets no definition of COmmunism I’ve ever heard.
Utopian Communism: Definitely not. Not utopia, not community.
Marxism: Nope. State is definitely not withering away. No rise of the proletariat to kill everyone.
Leninism: The Party hasn’t taken the sole power.
Maoism: The same…
Whether or not they fund education is irrelevant, because educaiton is not Communist. It is wholly irrelevant to Communist theory. Even Marx, who spent his last years teaching the proletariat, did so only because he felt it would make the inevitable bloodbath less terrible. In fact, every Communist power has risen to power on the backs of largely uneducated peasants and workers.
I’m sure they call themselves Communist. However, by your wn words, you show that they do not meet any of the classic or modern definitions of Communism. It sounds not too dissimilar from any other half-socialist state in the West.