Infer return type from generic types

I want to infer a type in a specific situation to either get a Box<T> or a T, based on an input parameter, but I end up with Box<unknown> and unknown instead. I think it is because of my usage of W extends Wrap<T>, but I don't know how to express this better.

See this code example, hover over boxResult and noBoxResult to see the inferred types are not ideal for me:

// Type definitions

interface ComplicatedDataContainer<T> {
    // contains many Ts in some complicated fashion
}
interface WrapA<T> {
    v: ComplicatedDataContainer<T>,
    p: "Box"
}
interface WrapB<T> {
    v: ComplicatedDataContainer<T>,
    p: "NoBox"
}
type Wrap<T> = WrapA<T> | WrapB<T>;

type Box<T> = {
    t: T
}

type SelectThing = <T, W extends Wrap<T>>(id: string, w: W) => W extends {p: "Box"} ? Box<T> : T

// Usage example

const wBox: WrapA<string> = {
    v: "",
    p: "Box"
}

const wNoBox: WrapB<string> = {
    v: "",
    p: "NoBox"
}

const selector: SelectThing = (id: string, w: Wrap<any>) => {throw new Error()}; // dont care about runtime behavior here, real impls are way more complicated

// I want the type of this to be Box<string>, but it is Box<unknown>
const boxResult = selector("", wBox);
// I want the type of this to be string, but it is unknown
const noBoxResult = selector("", wNoBox);

You can run this example here.

The problem is that there's no inference site for T so it defaults to unknown. Actually you don't need a separate type parameter T here, since it can be derived from the type parameter W. The Unwrap type below does this derivation.

type Unwrap<W extends Wrap<any>> = W extends Wrap<infer T> ? T : never

type SelectThing =
    <W extends Wrap<any>>(id: string, w: W) => W extends {p: "Box"} ? Box<Unwrap<W>> : Unwrap<W>

Playground Link

Note that I had to fill in ComplicatedDataContainer in the example so that it depends on T in some way, to avoid unintended structural equivalence.