yes, you can still use signal, molly and signal-foss. I have signal on my desktop and some of my family have molly and some signal-Foss.
The signal servers are primarily hosted on AWS with redundancies on Azure or Google Cloud. Molly and Siganl-FOSS use these too.
The official Android app generally uses the proprietary Google Play Services, although it is designed to be able to work without them.
Hence we use the signal-FOSS and Molly on our phones that do not have any google services.
Like any AOSP rom, Lineage, there are no google play services.
Its the google firebase that manages push notifications that seems to be the main privacy issue.
MollySocket allows getting signal notifications via UnifiedPush, not google firebase,
I only use Lineage and have done so for years without any problems since CyanogenMod 10.1.
Do remember that it is the choice of the developers to use google services and nothing to do with google.
When you say “Le Chat”, do you mean Mistral AI assistant/chatbot? Its probably stopped working since GPT‑5.
Currently it is not possible to run “Le Chat” ai on a phone without google,
Again its the devopers choice. They could develop a non-google Le Chat.
who on earth needs a chatbot on a phone?
I have never have any problems finding open source alternative apps.
MAPS: Comaps, Organic Maps and MagicEarth, all provide Turn by Turn navigation
https://en.wikipedia.org/wiki/Turn-by-turn_navigation
I dont use any Banking Apps. Why do you need a banking app? I login to my bank in the comfort and safety of my home.
Lineage:
https://wiki.lineageos.org/devices/
If you must use google try E/OS. It Uses MicroG and works very well.
microG is a FLOSS implementation of Google play services
https://doc.e.foundation/