Scoot leaves from T1 (think OP wrote T3, may have been a typo) as does JL, SQ is T2 for flights to Indonesia. Even if it was necessary, as advised by lokijuh, the switch of terminals or even simply passing through immigration in SIN and then re-entering airside is no big deal and super efficient and fast (assuming you travel on a US passport).

With Scoot, if you want ScootBiz (a Premium Eco / US Domestic F type seat) only TR280/288 are currently scheduled to be operated by a B788/789 and will have that option. If the flight is operated by an A321 or so, it won't have ScootBiz and will be all Eco seating.

SQ is a fully flat (regional) Biz seat and full service obviously plus lounge access in SIN. With Scoot you would need to get lounge access separately like using Priority Pass or such. Changi is one of the best airports in the world to make a connection. Just leave a decent buffer between your flights if on two tickets. Not because Changi takes long to connect (or exit and re-enter), but to cater for delays of your inbound flight from the US.