You should use existing useUser hook instead of adding userData here.

Do you think, we need additional request to api/users/me?

useUser hook provides all the information about authorized user. And you can access this data when you need it.
It is common practice to use this hook. And it's no need to duplicate the logic of getting user id.
And we get that information via request to api/users/me.

When I as authorized user put smth to the searchpage and press enter iuseProvideAuth sends the request to api/users/me. So I use it. If I'll use useUser it will send this request again.

So we have duplicated logic in our code)
I'd recommend to wait for Oleg review

I can change code, but I'm not sure in this solution. We are waiting for Oleg))

We have useUser hook. My proposition is to use it instead of adding userData in useProvideAuth.

I agree with @Lvyshnevska , inside a useUser hook we utilize a useSWR which should cache fetched data and prevent second API call. There is no need to call /api/auth/users/me/ the second time if it was already called and cached in the useUser

Ok. Done. But both hooks useUser and useProvideAuth use the same request /api/auth/users/me/ to the backend. Is it ok? I mean if I can use only useUser to check authenticated user or not and to get his data (id for my case), why do we need useProvideAuth?

As far as what I see we return different values from these hooks. But since they use the same API I assume that we can combine them both into one hook. Also, we do not use SWR in useProvideAuth that's something that could be fixed