Can typescript infer nested values from a function argument?

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I want to switch which args are passed, based on on the target. It seems like typescript can't infer what is passed in the function argument. Is there a way to help it figure out / write it differently so that it can infer it ?

Currently it is making a union out of all the passed arguments, but I would like it to pick out the correct argument.

const allowedTargets = {
    A: ({hiA}: {hiA: string})=>{},
    B: ({hiB}: {hiB: number})=>{},
}

type AllowedT = "A" | "B"

type ArgsOf<T extends AllowedT> = Parameters<typeof allowedTargets[T]>[0]

type Target<T extends AllowedT> = {target: T, args: ArgsOf<T> }

type TargetContainer<T extends AllowedT> = Record<string, Target<T>>

type MyFn = <T extends AllowedT>(arg0: TargetContainer<T>) => void

const myFn: MyFn = ()=>{}

// args are a union of all possible args
myFn({"hiA": {target: "A", args: {hiA: ""}}, "hiB": {target: "B", args: {hiA: ""}}})