Actually I want to post my solution here, thanks for the help from ZaidMalek.

As for the official documentation on Routing, it seems that we need to add the route of api.php in bootstrap/app.php. So the code in app.php would be:

<?php

use Illuminate\Foundation\Application;
use Illuminate\Foundation\Configuration\Exceptions;
use Illuminate\Foundation\Configuration\Middleware;

return Application::configure(basePath: dirname(__DIR__))
    ->withRouting(
        web: __DIR__.'/../routes/web.php',
        api: __DIR__.'/../routes/api.php', 
        commands: __DIR__.'/../routes/console.php',
        health: '/up',
    )
    ->withMiddleware(function (Middleware $middleware) {
        //
    })
    ->withExceptions(function (Exceptions $exceptions) {
        //
    })->create();