lvpha Google's stock OS is not really AOSP. Like all vendor Android variants (and third-party open-source variants such as GrapheneOS), Google's stock OS is derived from AOSP but quite different.
lvpha I wanted to know if GraphenOS has indeed improved battery life. Or does the security come at the cost of the battery?
Different users with different workloads and application mixes report different things. If sandboxed Google Play is running in two different user profiles on GrapheneOS, it may use more battery than a single instance would on Google's stock OS. GrapheneOS users who don't install Google Play and don't use a lot of apps often report better battery life than on the stock OS, because less code is running.
lvpha Also, how is compactgms compares to the original 800mg Google play services?
I'm not sure what is meant by "compactgms", but when Google Play is installed on GrapheneOS it is the actual code from Google.