Can Apple Watch be set up to inform me IMMEDIATLY when I'm separated from my phone?

Immediately? To my knowledge, there is no setting to accomplish this. This link explains how to set it up and if there were such a setting, it would be spelled out, but there isn't one --> Set up and use Notify When Left Behind in the Find My app - Apple Support

You can let Apple know this is something you'd like to see in a future update, by providing feedback here --> Product Feedback - Apple

I just got a notification I had left my iPhone behind as it was at my desk and I had gone outside for a few minutes. I think I had been away from my desk for 10 - 15 minutes before I got the notification on my watch. And it isn't honestly consistent as I often go for a quick walk around the building and I don't get a left behind notification every time.

I do not know if it is a "Time" thing, or a "Distance" thing, but when going for a walk, my Wife gets notified about a quarter of a mile from the house (0.4KM).