SQ check-in staff at SIN will be able to and most likely also be willing to tag checked bags to final destination if you show them your TK ticket from from IST to final destination. Hence, you do not need to enter Turkey to collect your checked bags on the luggage belts.

Upon arrival IST, you follow the signs for "international transfers" and pass through the main boarding pass and security checks before you reach departures level and the gate of your TK flight to your final destination. No issue at all.