VPN apps are notorious for significant battery drain due to their continuous need to encrypt/decrypt traffic and that cannot be helped. What can make a difference is if you need VPN all the time. At home, my ASUS router is connected to Mullvad VPN, so I don't need to run the VPN on my phone, but when I'm out and about on cell network, you bet I'm using a VPN!
Here's a great way to tell which apps are sucking your phone's battery dry. Turn on Developer Mode and check Running Services.
Turn On Developer Mode
Settings > About Phone > Build number > tap 7 times consecutively and Developer Mode will be enabled.
Check Running Services
Settings > System > Developer options > Running services
What you'll see are the current foreground apps, that is, apps actively consuming the battery.
In the upper-right corner of the screen, you'll see the "triple dots", and when you click on it, you'll see "Show cached processes." These are apps running in the background that are also consuming battery but at a slower rate. For example, I use Pulse SMS for texting, but since I'm not using it at the moment, it's waiting for an inbound SMS, so it sits in cached processes, but it still consumes battery. Any application whose Battery is Optimized can be a cached app. The goal is to get as few apps as possible running in cached processes. I'm preparing a very long post on the battery optimization I've done and how I achieved it.
All that said, the Pixel 6 was not my favorite phone for battery optimization. I have a 5a 5G (best overall), 6, 6a (meh), and 7 Pro (very good). I think if we worked together, we might be able to get your battery to last much longer.