Here's a bit of history. MAA is getting upgraded right now. T1 and T4 will be used for domestic flights. T4 exclusively for TATA airlines (Air India, Air India Express + Air Asia India, Vistara)
T2 is the newly built integrated terminal (but only for international flights) which has taken over all international operations from T3 + T4 and does not have a proper lounge. It has a makeshift Plaza premium lounge (for now). The Maharaja lounge that was situated in the older terminal cannot be used right now. Phase 2 of the upgrade project is to demolish T3 and build a new international terminal to boost capacity which is going to start in a while. I am not aware of any contract lounges there. Things may change before Dec 2023 and from initial reviews T2 seems to be a better terminal than T3 and T4. Hope I've answered all your questions.