They don't. However, Changi can transfer the bags for you. You will need to head to transfer desk at T1 transit and they can retag your bags (airport staff collect and re-tag bag for you). I asked the airport this question for SQ to QF flight (tho SQ technically interline with QF) later this year and was assured by the airport that they do this. Worth giving Changi a ring to confirm for your combo of flights. It is one of the few airports in the world offering this service. I have done this in the past with SQ to BA via the airport as well. Ofc, the alternative should work also and you should be ok to enter SG and re-check bags at T1 counter given your layover time, should you not trust the process. Still worth considering having the airport do it, should your SQ flight be delayed.