Window Alarms?

My sister purchased an older house with windows/window sills that are made out of wood. As a result, some of them don’t latch very well. I want to find her a cheap alarm system- I’m seeing a lot online that are magnetic and go off if the window is open. But would those work if her window is usually at least a little cracked open (because it doesn’t shut at all?)

Ideally, I’d like something that:

-works even if the window is cracked, and can alert her if it’s opened up even more

-something with a remote or an app, as opposed to having to set the individual sensors from “off” to “on” every night

-something with an alarm. A lot of the Smart sensors I’m seeing only send you a notification to your phone. We want one that will make noise if the window is opened.