Endpoints in Program.cs work but not in Controller

I have a small .NET Core test program, running in a Debian CT on Proxmox at 192.168.1.200:5000. When I test the API with Postman, the /test endpoint works. On the same machine as well as on other machines in the same network. But when I test /api/greet from my controller, I get an error http 404. Any idea why?

Here the successfull /test and the unsuccessfull /api/greet:
/test 200 OK
/api/greet 404 Not Found

Program.cs:

var builder = WebApplication.CreateBuilder(args);

builder.Services.AddControllers();

var app = builder.Build();

app.UseRouting();
app.UseEndpoints(endpoints =>
{
    endpoints.MapControllers();
});

app.MapGet("/test", () => "Test route reached");
app.Run();

Controller.cs:

namespace HelloWorldApi.Controllers
{
    [ApiController]
    [Route("api")]
    public class HelloWorldController : ControllerBase
    {
        [HttpGet("greet")]
        public IActionResult GetGreeting()
        {
            return Ok("Hello World");
        }
    }
}

I tried other ports, I deleted the whole code and wrote it again, I even used code from an old project that worked. Even if I put a Console.WriteLine("test") into the Constructor of the Controller, it doesn't get printed, so somehow the Controller does not get initialized?

In Program.cs you need to call

builder.Services.AddControllers();

and then after

var app = builder.Build();

do:

app.MapControllers()

Also to ensure that endpoints to your controller works add Route attribute like this:

[ApiController]
[Route("api/[controller]/[action]")]
public class HelloWorldController : ControllerBase
{
    public IActionResult GetGreeting()
    {
        return Ok("Hello World");
    }
}