Do I need to clear local storage on the frontend if my laravel controller logout() is handling the logging out of a user?

I have a function in my controller that's supposed to log a user out. It returns a success message upon clicking Logout on the frontend. My question is, on the JS side, do I need to clear local storage?

I'm asking this because upon refreshing my page after a successful logout and landing on the login screen (when logging out, the user gets redirected from the dashboard to the login screen) - I get sent back to dashboard which to me indicates that my logout function isn't working as intended (or is it?).

Am I doing something wrong?

Here's my controller code:

public function logout(Request $request) {

    try {
        $this->_usersRepository->userLogout();
        $loggedOut = $this->_usersRepository->userLogout()->getStatusCode();

        if($loggedOut != 200) {
            return response()->json(['message' => 'Error while logging out!'], 500);
        }
        return response()->json([
            'message' => 'Successfully logged out',
            'loggedOut' => $loggedOut
        ]);
    } catch (\Exception $e) {
        Log::error($e->getMessage());
        throw new \Exception($e->getMessage(), $e->getCode(), $e);
    }

}

Respository code for deleting oauth_access_tokens in the DB:

public function userLogout() {
    DB::table('oauth_access_tokens')->where('user_id', Auth::id())->delete();
    return response()->json(['message' => 'User successfully signed out'], 200);
}

source https://stackoverflow.com/questions/68966884/do-i-need-to-clear-local-storage-on-the-frontend-if-my-laravel-controller-logout