No, Stanley didn't murder Peter
He committed suicide, just
Stanley murdering Peter is completely unnecessary in terms of story. In fact, it cheapens the concept of the character.
Someone driven to suicide by her - and her "why did this have to happen to ME?" reaction - is consistent with everything we know about her. She leaves ruin in her wake, but through complete solipsism, not through targeted evil. Everything is about her. In a perverse way, taking the time to murder someone would be a character break - she'd have to stop focusing on herself long enough to bother murdering someone else.
People die because of tornadoes, but tornadoes don't murder people. It's inevitable, but completely impersonal.
Stanley is truly shocked at the suicide, in the same way a selfish child would be shocked if one of her toys suddenly got up and walked away. She may have smashed it in passing; she may have been completely culpable; but she didn't target it for murder. These things just happen around her.
In terms of a narrative arc, murder is an act by a different kind of character in a different plot. This story is complete and consistent without it.
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Nothing to see here, move along.