If you want chrome and chromedriver to stay open, you have to use the ‘detach’ option when starting chromedriver.
In your case add :
from selenium.webdriver.chrome.options import Options
chrome_options = Options()
chrome_options.add_experimental_option("detach", True)
before you pass in the options to the browser
browser = webdriver.Chrome('drivers/chromedriver.exe', chrome_options=chrome_options)
Or you can run the code in debug mode with breakpoint at the end and when it pauses ‘kill’ the program and take over the browser if you want to, but this works in IDE only.
EDIT – added the import for clarity