Either I need the app to forward any received text message to another phone number. This should be reliable, i.e. not stop when the phone is idle/sleeping.

Or, I need to sync all received message to a cloud, Nextcloud, Google Account, proprietary; so that I can read message from another device. This needs to be reasonable secure, i.e. either e2e encrypted or stored to trusted service. I'm willing to trust Nextcloud or google for the purpose. I'm also willing to trust a third-party service when run professionally, but I'm sceptical.