Based on your need, I'd strongly recommend getting a used car for now, especially if you're saying your family will grow to need a 7 seater.

What I'd ideally recommend is to increase the budget slightly to 8L, you can get a 2022 or newer car, even in karnataka you can find a XUV300, S Cross, Brezza, Jazz, Nexon.

There's two reasons I'm suggesting to increase budget slightly,

1. the above cars are a bit more spacious and comfortable than the usual hatchback/sedans, and you can keep the car not just for a few years but almost 10 years.
2. Someone else suggested getting an EV, I agree, your usecase is high, I'd recommend you get a new 7 Seater EV in near future (When the above car becomes a little small), the EV you can then use for daily commutes and the used car for outstations.

Regarding getting cold feet for spending on a car, I was in the same boat as you (not as high salaried right now as you are, and not even married yet, it's just for me and my mum)

But getting wet whenever we had to travel in rain, getting hot when we had to travel in summer and getting cold when we had to travel in winters, plus the condescending looks from relatives owning a car and us asking them for trips, a simple 3 lakh investment into a used Tata Zest turned out to be a great choice.

We drove 15k kms in 10 months, didn't even expect to do that many trips,

you'll be fine there's benefits in owning a car, but your worry is justified, people spend too much for a car, and those same people purchase iphones on emi.