Having everything on the phone automagically synced is probably something far into the future. But for some data, you can already set it up yourself. It’s just not a “unified experience”…
Chat history is a first class citizen in Matrix, so messages would appear on your new phone. (You have to trust your home server, I think.) Not sure about XMPP and IRC, or if Matrix on the Librem 5 will also cover SMS.
Phone book entries and calendar events can be synced using CalDAV/CardDAV. Normally, you need to trust the server, but EteSync provides an alternative where all data is encrypted before leaving the device. See this comment with links:
EteSync is available for desktop use (in addition to an Android app and a web app). I believe it should be easy to add to the Librem 5.
Photos, videos, documents and files in general could be synced using Syncthing:
Syncthing replaces proprietary sync and cloud services with something open, trustworthy and decentralized. Your data is your data alone and you deserve to choose where it is stored, if it is shared with some third party and how it’s transmitted over the Internet.
You still need to trust the “server”, though. Any computer, and any number of computers, can be a Syncthing peer, including your laptop.