It's not difficult - unless I'm missing something?

Get off plane. Walk to lounge (The Private Room, since your connecting flight is in Suites). You won't know what terminal your flight arrives at until just before landing, but as all terminals are linked airside at SIN it doesn't matter. Show boarding pass/lounge invitation for onward flight.

Then once you have had enough and want to go to your hotel, exit the lounge and walk to hotel.

Rinse and repeat later that day once you check out of the hotel and want to hang out in the lounge before your flight departs.