Why does mutate with value null not propagate between tabs?

[florianwalther-private]

I use SWR to handle the currently logged-in user.
A user log-in successfully updates other windows on refocus. A log-out does not. Why is that?

export function useUser() {
    const { data, error } = useSWR(
        "http://localhost:5000/api/users", async (url: string) => {
            const response = await fetchData(url);
            return response.json();
        },
        {
            shouldRetryOnError(err) {
                return !(err instanceof UnauthorizedError)
            },
        }
    );
    return {
        user: data as User | undefined | null,
        userLoading: !error && !data,
        userLoadingError: error,
    }
}

Why does this not propagate between windows:

 async function logout() {
        try {
            await BlogApi.logout();
            mutate('http://localhost:5000/api/users', null);
        } [...]
    }