Javascript – React context updates in parent component, but for child components it's still undefined

So I have a problem with useContext in React. I want to update it in my parent component, then use it in child components. However, while the context seem to work properly inside my parent component, when I want to use it in the children, it’s undefined (still has its default value).

The code snippets that illustrate the problem:

LobbyContext.tsx

import React, {createContext, useState} from "react";
import { ILobby } from "@/components/GameIndex";

interface ILobbyContext {
    lobby: ILobby | undefined;
    setLobby: React.Dispatch<React.SetStateAction<ILobby | undefined>>;
}

export const LobbyContext = createContext<ILobbyContext>({
    lobby: "",
    setLobby: () => {
        console.log("old function")}
});

export function LobbyProvider({ children }: { children: React.ReactNode }) {
    const [lobby, setLobby] = useState<ILobby | undefined>();

    return (
        <LobbyContext.Provider value={{ lobby, setLobby }}>
            {children}
        </LobbyContext.Provider>
    );
}

/game/[id].tsx

import {LobbyProvider} from "@/context/LobbyContext";
import GameIndex from "@/components/GameIndex"
const Index = () => {

    return (
            <LobbyProvider>
                <GameIndex />
            </LobbyProvider>
    );
};

export default Index;

fragments of GameIndex.tsx

const { lobby, setLobby } = useContext(LobbyContext);

/*...*/

useEffect(() => {
            fetch(`http://localhost:8080/api/lobby/${lobbyId}`)
        .then(data => {
            setLobby(data);
        }
, [lobby, setLobby] }

/*...*/

    return (
       {lobby !== undefined ? <Scoreboard/> : <div>Loading...</div>}
    );

Scoreboard.tsx

import {LobbyContext} from "@/context/LobbyContext";

const Scoreboard = () => {
    const {lobby, setLobby} = useContext(LobbyContext);

return (
        <div className={"scoreboard flex-col"}>
        {lobby}
        </div>
    );
}

ironically, Scoreboard renders, because lobby is defined inside of GameIndex.tsx, but inside of Scoreboard, it’s undefined…

What am I doing wrong?