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Do I need a transit visa to collect baggage and then check-in again with AirIndia?
Yes. A self transfer is the same as two individual flights that just happen on the same day. You will need proper credentials to enter Kuwait.
Can I rely on NAS Kuwait to do that?
If you are planning to book a "meet & assist" service your best bet is to ask the provider directly. You can check https://pearlassist.com/kuwait-kwi-intl-kuwait-kuwait for "standard" services but it's not clear whether they would support "self-transfer" since that includes moving luggage (which transit typically doesn't).
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Do I need a transit visa to collect baggage and then check-in again with AirIndia?
There is no concept of transit visa for Indian passport holders in Kuwait. You will need a valid entry visa (and only business visas are being issued currently). You will have to collect bags yourself and check in again at Departure level.
Can I rely on NAS Kuwait to do that?
No, they wont assist with this.