If your phone is locked you will most likely not get the notifications, it just depends on the app. I do agree it can waste battery.

It's important to remember this is only a concern on non-free apps. The FOSS apps have very low power background services that check for notifications without the app running.

I use /e/os. It is based on LineageOS, is completely de-googled and has MicroG integrated. MicroG means push notifications with apps like WhatsApp will work. https://e.foundation/