If you're curious about battery life on stock vs. GOS, I ran a 2-month long comparative analysis on how each OS performs on Pixel 8, which is available here.
My conclusion was that with my setup, which uses a single owner account profile that uses Shelter to compartmentalize using a separate work profile within the owner account profile that has sandboxed Google Play Services installed in both profiles, GOS gets slightly worse battery life than I did on stock.
Knowledgeable users have noted that I'm getting worse battery life on GOS because I have two instances of GmsCompat
running at all times and have hypothesized that only having one instance of GmsCompat
would give me better battery life compared to stock.
Of note, even with this relatively worse battery life, I am still able to get more than 9 hours of SOT (screen on-time) on GOS, which is phenomenal battery life.
I haven't been able to test out that hypothesis as my compartmentalization needs are best met by my current setup, but I wouldn't let your concerns about battery life keep you from getting a P8 to use GOS.
For your other concerns, I have not had any display stuttering or any other major issues when using my P8. The one issue I had is that the navigation bar occasionally gets stuck at the side, and I've seen this happen on both stock and on GOS. But it's rare (maybe once a month or two), is purely cosmetic, and is easily fixed by a soft reset.