There is no GOS messaging app, it's just the AOSP SMS/MMS app by default and is due to be replaced one day.
SMS/MMS is not secure / private whatever the app you use. RCS is a walled garden controlled by phone operators and only Google offers E2EE but doesn't encrypt metadata and gets lots of telemetry, it's essentially a disappointing option against another disappointing option, but I'd probably go for Google Messages if you can get RCS E2EE to work on GOS.
The general recommendation from GOS is to use Molly which is a hardened fork of Signal, the Signal app like the WhatsApp app has a lot of attack surface.