There are transit storage options airside at Changi, refer to the following:
https://www.changiairport.com/en/air...e-storage.html

MH allows 1 carry-on, plus either: 1 briefcase, handbag (male/female), notebook or a laptop computer bag, OR small camera bag.

Depending on how overweight and bulky (particularly the backpack), you might be allowed to carry both bags on.

If obviously overweight / bulky, I’d just check or store one. Plan to keep the backpack under the seat - it’d only be an hour.

I seem to remember MH sticking a ‘carry-on’ tag on such bags’ handles on some flights, I guess to try limit multiple bag for a single passenger - not sure of this practice on SIN-KUL.