Many different points to address here.
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On average for tier 3 college, I think you are making good at 7 LPA. If you like frontend engineering then I will recommend you to stick to it rather than going for an MBA. MBA will push you into a totally different career track and it would be difficult to go back to frontend or software engineering in general.
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You haven't mentioned whether you want to do a Masters in India or abroad. If it's possible, try doing it abroad and work towards getting a scholarship. There are many good options from the usual US (though very expensive) to the UK, Europe, Australia or Singapore. Others are much more affordable.
It is always beneficial to have about 2-3 years of experience before doing the Masters. I think about 2 years can be enough time for you to really explore your likes and dislikes about the software field. During this time, you can also explore different fields like backend, machine learning, data science, AR/VR development. One advantage with foreign Masters is that you have much more flexibility in choosing courses and you can specialize in these fields of your choosing.
All hinges on whether you like the field or not. If you like it you can work in it for a few years and then still choose to move to the management track as a tech focused Product Manager even without an MBA. According to me, being a PM with prior tr ch experience is absolutely a big advantage.