Question about context propagation

Say we have structure like this,

routes/
    __root.tsx
    index.tsx
    $id/
        edit/
            index.tsx

routes/
    __root.tsx
    index.tsx
    $id/
        edit/
            index.tsx

routes/
    __root.tsx
    index.tsx
    $id/
        edit/
            index.tsx

routes/
    __root.tsx
    index.tsx
    $id/
        edit/
            index.tsx

I want to inject context from the root index.tsx (

) like this.

createFileRoute("/")({
  context: () => ({hello: "world"}),
})

createFileRoute("/")({
  context: () => ({hello: "world"}),
})

createFileRoute("/")({
  context: () => ({hello: "world"}),
})

createFileRoute("/")({
  context: () => ({hello: "world"}),
})

I want to use that context in say,

/1/edit/

/1/edit/

/1/edit/

/1/edit/ with

const context = Route.useRouterContext()

const context = Route.useRouterContext()

const context = Route.useRouterContext()

const context = Route.useRouterContext()

But it seems I cannot access the context variable

hello

hello

hello

hello. Does context only propagates to child routes when injected in layouts?