Laravel 9 with breeze & react, Auth::check() always returning false

Question

I installed Laravel 9 with breeze and react.
In the react page, I call this api and it needs to check the user is logged in.

Wishbox.jsx

axios
    .post("/api/add/wishlist", {
      prd_no: event.target.getAttribute("productno"),
      mem_id: 1,
    })

At first, I tried to add middleware in the routes/api.php like this.

Route::post('/add/wishlist', [App\Http\Controllers\UserController::class, 'addWishlist'])->middleware('auth');

Unfortunately, it didn't work at all and couldn't find out why.
It just kept giving me the error 401 Unauthenticated.

So I removed the middleware part from the route, then decided to check in the controller side, like this.
UserController.php

public function addWishlist(Request $request) {
        dd(Auth::guard('web')->check());
...

but it just keep returning false, even though I already logged in. Without the guard('web') part, the result is same.

And If I go back to / (Home) route for just checking I am logged in, it looks like I didn't log in. But I just logged in! Right before I press the button to go previous page in the browser. So I refreshed the page, then it says I am logged in.
I really don't understand why it works like this.

Please anyone guide me to understand what's happening here and what did I miss or wrong here.