Would it make sense to use the combination of AMEX True Cashback + GrabPay to pay for things or just use a POSB Everyday Card?

AMEX TCB + GPMC is a more all-encompassing approach, in that you get decent rewards for any type of spending and are not limited to specific categories.

POSB Everyday has pretty good rebates only for selected merchants (ie groceries), but for many other categories, it's almost not worth using.

If you want to keep it simple, I'd say AMEX TCB + GPMC is the better approach. If you don't mind juggling between the 2 methods and can remember which transactions Everyday is better for, then you can use both.

But I probably wouldn't use Everyday only.