Mutlidimensional associative arrays in typescript

I am trying to use a multidimensional associative array that was passed from php to the frontend so I have created a new type as follows:

type AssociativeArray<T = unknown> = { [key: string]: AssociativeArray<T> | T | undefined | T[] };

When I try to compile the following code:

type AssociativeArray<T = unknown> = { [key: string]: AssociativeArray<T> | T | undefined | T[] };

const exampleStatusJSON: AssociativeArray<string> = {
  available: "true",
  username: "Jean-loup",
  house: {
    room: {
      name: "Highcrest",
    },
  }
};

if ((typeof (exampleStatusJSON["house"]) !== "undefined") &&
            (typeof (exampleStatusJSON["house"]["room"]) !== "undefined") &&
            (typeof (exampleStatusJSON["house"]["room"]["name"]) !== "undefined")) {
    console.log("OK");
}

Typescript playground

typescript throws an error in the second and third condition:

Element implicitly has an 'any' type because expression of type '"room"' can't be used to index type 'string | AssociativeArray<string> | string[]'.
Property 'room' does not exist on type 'string | AssociativeArray<string> | string[]'.(7053)

What would be the best way to describe such arrays in typescript?