Spring-Boot OpenAPI - @RestControllerAdvice not limited to methods throwing the Exception

Question

I need to document my SpringBoot APIs and their possible exceptions with OpenAPI, and I am using SpringDoc-OpenAPI https://springdoc.org/.

To handle the NotFound cases I created this exception class:

import org.springframework.http.HttpStatus;
import org.springframework.web.server.ResponseStatusException;

public class NotFoundException extends ResponseStatusException {
    public NotFoundException() {
        super(HttpStatus.NOT_FOUND);
    }
}

and this @RestControllerAdvice

import org.springframework.http.HttpStatus;
import org.springframework.http.ResponseEntity;
import org.springframework.web.bind.annotation.ExceptionHandler;
import org.springframework.web.bind.annotation.ResponseStatus;
import org.springframework.web.bind.annotation.RestControllerAdvice;

@RestControllerAdvice
public class GlobalControllerExceptionHandler {
    @ExceptionHandler(NotFoundException.class)
    @ResponseStatus(HttpStatus.NOT_FOUND)
    public ResponseEntity<String> handleNotFoundException(RuntimeException ex) {
        return new ResponseEntity<>(ex.getMessage(), HttpStatus.NOT_FOUND);
    }
}

The problem I am facing is that the generated OpenAPI yaml file has

  responses:
    "404":
      description: Not Found
      content:
        '*/*':
          schema:
            type: string

for all @RestController endpoints, instead of only for the methods with throws NotFoundException.

How can I limit the @ControllerAdvice (or the OpenAPI), to generate the 404 Response documentation only for methods with the throwing signature?

Do I need to use something else other than the @RestControllerAdvice? I would like to avoid having to annotate every single method.