Selenium / select dropbox?

i try to use selenium with this site:

https://gesund.bund.de/suchen/aerztinnen-und-aerzte

with the following code:

import time
import os, sys

from selenium import webdriver
from selenium.webdriver.chrome.options import Options
from selenium.webdriver.chrome.service import Service
from selenium.webdriver.support.ui import WebDriverWait
from selenium.webdriver.support import expected_conditions as EC
from selenium.webdriver.common.by import By
from selenium.webdriver.support.ui import Select
from webdriver_manager.chrome import ChromeDriverManager
# from fake_useragent import UserAgent

if __name__ == '__main__':
  path = os.path.abspath(os.path.dirname(sys.argv[0]))

  options = Options()
  options.add_argument("start-maximized")
  options.add_experimental_option("prefs", {"profile.default_content_setting_values.notifications": 1})
  options.add_experimental_option("excludeSwitches", ["enable-automation"])
  options.add_experimental_option('excludeSwitches', ['enable-logging'])
  options.add_experimental_option('useAutomationExtension', False)
  options.add_argument('--disable-blink-features=AutomationControlled')
  srv=Service(ChromeDriverManager().install())
  driver = webdriver.Chrome (service=srv, options=options)
  waitWD = WebDriverWait (driver, 10)

  link = f"https://gesund.bund.de/suchen/aerztinnen-und-aerzte"  
  driver.get (link)
  waitWD.until(EC.presence_of_element_located((By.XPATH,'//input[@id="arztsuche__field_where"]'))).clear()
  time.sleep(0.5)
  waitWD.until(EC.presence_of_element_located((By.XPATH,'//input[@id="arztsuche__field_where"]'))).send_keys("13403")
  time.sleep(0.5)

  # select = Select(driver.find_element(By.XPATH,'//div[@id="arztsuche-fachrichtung-list"]'))
  # driver.execute_script("arguments[0].click();", waitWD.until(EC.element_to_be_clickable((By.XPATH, '//div[@id="arztsuche-fachrichtung-list"]'))))    
  waitWD.until(EC.presence_of_element_located((By.XPATH,'//div[@id="arztsuche-fachrichtung-list"]'))).send_keys("Hausarzt")    

input("Press!")

I try to select an entry from the combobox "Fachrichtung" i the middle but it is not working. I tried several thing like you can see in the comment:

  # select = Select(driver.find_element(By.XPATH,'//div[@id="arztsuche-fachrichtung-list"]'))
  # driver.execute_script("arguments[0].click();", waitWD.until(EC.element_to_be_clickable((By.XPATH, '//div[@id="arztsuche-fachrichtung-list"]'))))    
  waitWD.until(EC.presence_of_element_located((By.XPATH,'//div[@id="arztsuche-fachrichtung-list"]'))).send_keys("Hausarzt") 

Tried to use select (but it tells me its no select-element). Tried to click on it - but it is not clickable. And tried to simple assign a text to it - but this is also not working.

How can i automate the element on this site?

It is an Auto Complete form,Select won't work here.
You need to identify the element and then click on the element after search result appear on the autocomplete form.

waitWD = WebDriverWait (driver, 10)

link = "https://gesund.bund.de/suchen/aerztinnen-und-aerzte"  
driver.get (link)
searchstring="13403"
waitWD.until(EC.element_to_be_clickable((By.XPATH,'//input[@id="arztsuche__field_where"]'))).clear()
time.sleep(0.5)
waitWD.until(EC.element_to_be_clickable((By.XPATH,'//input[@id="arztsuche__field_where"]'))).send_keys(searchstring)
time.sleep(0.5)
waitWD.until(EC.element_to_be_clickable((By.XPATH,"//span[text()='{}']".format(searchstring)))).click()

Browser Snapshot:

UPDATE:

waitWD = WebDriverWait (driver, 10)

link = "https://gesund.bund.de/suchen/aerztinnen-und-aerzte"  
driver.get (link)
searchstring="13403"
waitWD.until(EC.element_to_be_clickable((By.XPATH,'//input[@id="arztsuche__field_where"]'))).clear()
time.sleep(0.5)
waitWD.until(EC.element_to_be_clickable((By.XPATH,'//input[@id="arztsuche__field_where"]'))).send_keys(searchstring)
time.sleep(0.5)
waitWD.until(EC.element_to_be_clickable((By.XPATH,"//span[text()='{}']".format(searchstring)))).click()

waitWD.until(EC.element_to_be_clickable((By.CSS_SELECTOR,"input#arztsuche-fachrichtung"))).click()
secondField='Hausarzt'
waitWD.until(EC.element_to_be_clickable((By.XPATH,"//span[text()='{}']".format(secondField)))).click()

BrowserSnapshot