Silk Air flight followed by Singapore Airlines First Class flight on separate tickets - Can I check through my baggage?

Hi

Not sure how to explain but I’ll try my best. I will be flying Singapore to Melbourne first class however, my first leg of the flight will be from India (Chennai) to Singapore with silk air, and since Singapore doesn’t offer first class, seperate booking are required.
I booked chennai to Singapore through velocity and the first class through Singapore directly.
I do have over 12 hours layover (probably book a room to sleep), what I want to confirm is, am I required to exit immigration to reclaim my luggages and check in again or it simple go directly to Mel? Will there be any concerns or problems that may occur? Since booking a full leg kinda protects the flyer from any cancellation, delays etc

Shouldn't need to go get luggage, ask at check in at Chennai to book straight through. Keep a print out of both etickets

At Changi you will have access to the the private room lounge as you're flying SQ first.

I’ve had a few hours nap in there without issues and showered then gone out for meetings