EK can transfer bags to SQ, however if these are 2 separate bookings , there is no requirement that they do so

I would suggest that it would be sensible to get the transit visa in case you do need to enter Singapoer ( or if flight gets delayed and you have to spend night in Singapore )

if this is all on 1 ticket, then EK can ( and would be expected to ) transfer the bags onto the SQ flight