It's because of jurisdiction.
Normally, only states have jurisdiction over murders. The feds can charge murder if and only if the murder is connected to some other federal "crime of violence" (e.g. killing a federal official, murder-for-hire across state lines).
Here, the federal 'hook' was interstate stalking. But the federal stalking crime apparently isn't a "crime of violence" because you can stalk without intentional force.
Because the stalking charges don't legally qualify as "crimes of violence", the federal government doesn't have jurisdiction over the alleged murder.
What do you mean here? They usually get prosecuted by the state.
Because NY state law doesn't allow for the death penalty, and the federal government wanted the death penalty, they intentionally moved it to a federal jurisdiction.
There's a Twitter thread[0] that seems like a reasonable explanation.
[0] https://x.com/adamscochran/status/2017284770158485767 / https://xcancel.com/adamscochran/status/2017284770158485767