Norman
I installed Molly on a spare, P6a running standard G@@gle android, G@@gle everything is installed by default, and overnight on standby Molly consumed 37% of the battery consumption, it ran in the background for 50 minutes, there are no contacts in the phone, it was just used in this instance as a test bed for Molly, so who or what is Molly communicating with and burning through my battery...
Molly may be the messenger for you, you defend it admirably, but having used it in GrapheneOS on two different Pixels and used it on Pixels running G@@gle android, and running it on Samsung phones with G@@gle, my non scientific, but observational approach over years tells me Molly eats batteries. So I don't use it.