Modeling string template type

I have a type

type T = {
  foo: '' | `/${string}`
}

type T = {
  foo: '' | `/${string}`
}

type T = {
  foo: '' | `/${string}`
}

type T = {
  foo: '' | `/${string}`
}

which I have modelled with arkType as

const v = type({
    foo: '"" | /^\\/.*$/',
})

const v = type({
    foo: '"" | /^\\/.*$/',
})

const v = type({
    foo: '"" | /^\\/.*$/',
})

const v = type({
    foo: '"" | /^\\/.*$/',
})

Which seems like the same thing. But out infer type of

foo

foo

foo

foo is just

string

string

.

Just wondering if there is a way to model '' | `/${string}` that will give me that as an infer/out type?

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