L.R.
I have to guess that this is SIL's first child.
Is that right? Because if it is -- can you see why grandma is baby-crazy for her daughter's first child? It's not like SIL planned her baby's arrival to grab mom's attention from your baby.
I"m not asking you to love the idea that MIL's like this just now, but just to try to understand it. Many moms are closer to their daughters than their sons, and in that case, grandma is relishing the child of the adult child she's closer to. Is that a possibility you can see? Can you step back enough to take a deep breath and say, hey, this is annoying but understandable? Nervy Girl said, very rightly, that she hopes your MIL can gain some objectivity in time; I hope you can do the same.
It's also a vast leap to assume that she "doesn't like" your last baby. She is smitten with her daughter's kid right now. Polite? No, but are you going to make this a hill to die on? Is it worth a rift if you confront her? She likely has no idea at all that she's being so blatant in your eyes. Let it pass. Your baby has zero idea of being ignored and won't for some time to come. The novelty of SIL's baby may well wear off. Remember, your MIL has done a lot for you as you recognize in your post -- cared for all four of your other kids, shown up for all their events, etc. Your new baby doesn't have events yet and isn't old enough to stay at Grandma's for sleepovers. Wait it out.