Your loginUser function is attached to the <LoginBtn> click event. Assuming that component passes some kind of Event to the handler, it's probably an event triggered by a <button> (or similar) which is what is assigned to e.target. There won't be any username property.

What you should be doing here is have your username and password inputs be controlled components with their value tied to state

const [username, setUsername] = useState("");
const [password, setPassword] = useState("");

and

<input
  value={username}
  placeholder="example@mail.com"
  onChange={(e) => setUsername(e.target.value)}
/>
<input
  type="password"
  value={password}
  placeholder="******"
  onChange={(e) => setPassword(e.target.value)}
/>

Your loginUser context function should accept username and password strings instead of an event

const loginUser = async (username, password) => {
  const response = await fetch(
    "https://estudio-ghibli-2022.herokuapp.com/login",
    {
      method: "POST",
      headers: {
        "Content-Type": "application/json",
      },
      body: JSON.stringify({ username, password }),
    }
  );

  // don't forget to check for errors
  if (!response.ok) {
    throw response;
  }

  const data = await response.json();
  console.log("loginUser data:", data);
  // now do something with data ¯\_(ツ)_/¯
};

and

<LoginBtn
  type="button"
  onClick={(e) => { e.preventDefault(); loginUser(username, password); }
>Login</LoginBtn>

The problem is that you are trying to access the value of username and password fields from non existing properties in your loginUser function:

body: JSON.stringify({
  username: e.target.username.value,
  password: e.target.password.value,
})

I'm assuming that the param "e" is a React.MouseEvent because you are assigning loginUser as the handler of onClick event of the <LoginBtn> component:

<LoginBtn type="button"
          onClick={loginUser}>
  Login
</LoginBtn>

So unless you have a custom implementation in that component that somehow extracts this data from the form, there's a good chance that e.target points to an element that is not relevant for you to get this information.

So you could use Phil's suggested approach in the other answer using controlled components for the inputs to fix the issue or you could also set your handler to an onSubmit event of the form containing this elements and extract the information using FormData like this:

let loginUser = async (e) => {
  ...
  const formData = new FormData(e.target);
  const { username, password } = Object.fromEntries(formData.entries());

  let response = await fetch(..., {
    ...
    body: JSON.stringify({ username, password }),
  );
  ...
};

Assuming that <FormInner> has onSubmit event:

<FormInner onSubmit={loginUser}>