client: Store user id in authenticated user details.

Earlier we only stored the user name.
We need to store the id to be able to track whether it is
the current player's turn, show the Start Game button etc.

frontend/src/contexts/AuthContext.tsx

@@ -12,6 +12,7 @@ import { useLocation, useNavigate } from 'react-router-dom';
 
 export type User = {
     name: string;
+    id: string;
 };
 
 export type AuthContextProps = {
@@ -81,6 +82,7 @@ export function AuthProvider({ children }: { children: ReactElement }) {
                     // so the jwt was valid
                     setUser({
                         name: data.user.username,
+                        id: data.user._id,
                     });
                     authWith(localToken!, data.user._id);
                 }
@@ -118,6 +120,7 @@ export function AuthProvider({ children }: { children: ReactElement }) {
             console.log(data);
             setUser({
                 name: data.user.username,
+                id: data.user._id,
             });
             authWith(data.token, data.user._id);
         },