IMO, additional battery usage caused by an idle SIP app should be zero, just like WhatsApp, FaceTime, etc.
This is accomplished by push notifications. Switching to an app that uses it takes minimal setup and you can continue to use UDP if desired.
My current favorite is Groundwire, which sells for $10. Though there are quite a few negative reviews, I’ve never experienced any of the problems mentioned. One problem I do have is an incompatibility between my phone and car Bluetooth – one cannot answer a call from the car screen (if there’s a passenger, they can answer on the phone and you can use Bluetooth to talk). Unfortunately, other SIP apps I’ve tried have the same issue. If you buy it, test it thoroughly within the first 48 hours; if dissatisfied you can uninstall and request a refund.
One minor change was needed in FreePBX. I set Max Contacts to 4, as there are sometimes quirks when switching between local and push server registrations.
I have enjoyed Groundwire. I bought it before Clearly IP came out with Clearly Anywhere which we use for all of our mobile solutions now. (I believe Sangoma connect is also built from Groundwire as well)