Since at least 50% of the equation is what is your security alarm and how it’s connected to your home network or the Internet, it would be helpful to mention that. And whether there is an app for your security system that runs on an iOS or Android smartphone.
For example, I have a Ring Doorbell video cam. It’s sensitive to someone pressing the button or motion detection within its field of view according to zones that I can set, sensitivity, etc., in the Ring app. When there is a doorbell ring or motion detection, the Ring app on my phone will create a phone notification. My Samsung Galaxy Note 8 will pass the notification along to my Samsung Galaxy Gear S3 Frontier watch. The notification can be tuned to make a noise or vibrate, I believe
To have the alert function and real-time reaction from the doorbell and app, I don’t need to pay a subscription fee to Ring. But if I want the video cam on the doorbell to record what it sees, I need to pay Ring a $30 per year fee for cloud recording (with limited time storage of any videos recorded).
My watch can connect to my home Wi-Fi system independent of the phone but since Samsung has elected to run a special lean OS on its watches, I need the watch to interact through an Android smartphone running the Ring app, AFAIK.