Is there built in functionality for the Watch 3 to track my sleep patterns? Is there anything that figures out sleep cycles and duration, and tracks heart rate at the same time for a prelimnary analysis?
The Apple Watch doesn't currently have built-in sleep tracking functionality. However, there are some excellent third-party apps that can track your sleep. Sleep++ is one of the more popular options, and it's free. However, Sleep++ doesn't track heart rate itself, instead leaving you to use the Apple Health app's built-in heart rate tracker. Another great choice is Sleep Diary, which does track heart rate, and seems to have a wealth of features.
This is just from some quick research - I don't personally do any sleep tracking with my Apple Watch, as I charge it overnight.