WhatsApp is notorious for consuming a tremendous amount of battery resources. It never used to be this way, but since Meta purchased it, they have motives other than providing a messaging app. Meta gets its revenue from selling your personal information. All apps in the App Store have to disclose the information they can harvest and for WhatsApp, you can see that it gets:
- Purchases
- Location
- Contacts
- Financial Info
- Contact Info
- User Content
The Background App Refresh switch does not prevent all background tasks that an app is allowed to run. It just pertains to the background tasks that are responsible for updating the UI, so when you launch the app again, you will see these changes immediately. There are other background tasks that an app can run that allows it to communicate with their own servers.
As you have seen, Apple gives you the tools to evaluate the affects of each app on your device and the impact they have on battery consumption so you can make a decision on if you want to use the app. You have the option to contact the developer or remove the app. Meta has updated WhatsApp 8 times in the last month, with some correcting issues and also causing more problems. It may be the case, they are aware of this problem and attempting to correct it.