A fresh install of GrapheneOS has far lower idle power usage than the stock Pixel OS. Power usage while active is comparable. Making a similar setup to the stock Pixel OS by installing sandboxed Google Play and a couple dozen apps doing a bit of background work will result in similar battery life.
GrapheneOS doesn't come doesn't come with anything keeping open a push connection and barely has any scheduled work. Waking every 8 hours for update checks doesn't use significant power. It doesn't have better battery life due to any major efficiency improvements but rather the lack of bloatware.
Installing sandboxed Google Play on GrapheneOS results in having a push connection for Firebase Cloud Messaging and doing a lot more work in the background. Idle power usage will still tend to be better than the stock Pixel OS, but adding more apps to match their bloatware will make it comparable.
Battery life heavily varies based on apps, networks and OS configuration. Many people end up with far better battery life on GrapheneOS and many people end up with far worse battery life due to differences in how they set up their devices. It's easy to end up with either result with simple choices.
Installing Signal in a profile without sandboxed Google Play and granting the power optimization exception it requests is enough to destroy battery life and end up worse than the stock Pixel OS. The power efficient choices are either using Molly with UnifiedPush (Signal fork) or Signal with FCM.
Running both sandboxed Google Play and an efficient UnifiedPush app can have competitive battery life with the stock Pixel OS. Those should be the only 1-2 battery optimization exceptions for most users. Signal's fallback push will drain more power than all the bloatware in the stock OS itself.

On a Google Mobile Services OS, Play services is built into the OS as a highly privileged component with immense access and handles work across profiles.

Sandboxed Google Play are regular sandboxed apps without any special access. Each installation in a separate profile is entirely independent.

Setting up a work profile, Private Space and secondary user on the stock Pixel OS results in all 3 secondary profiles using the global Play services instance running in the Owner user for a shared FCM push connection, etc. Installing sandboxed Google Play in 4 profiles would run 4 FCM connections.
@GrapheneOS This is a bit confusing. Does this mean that FCM will work in secondary profiles if Play Services are installed in the Owner?

@Baffling7384 No, that's the opposite of what we said.

This is about how it works on a Google Mobile Services OS instead of the stock Pixel OS::

> Setting up a work profile, Private Space and secondary user on the stock Pixel OS results in all 3 secondary profiles using the global Play services instance running in the Owner user for a shared FCM push connection, etc.

We're explaining sandboxed Google Play are regular sandboxed apps which means it can't operate across profiles like that.