JFK
To back up your calendar and contacts, I recommend using a secure mail provider such as Tuta.com.
Or purely local use with a calendar app that works without the internet.
In this case, regularly exporting contacts from the Contacts app as a .vcf file would be sufficient (you can easily import them back into the Contacts app).
And appointments from calendar apps can be exported and imported as .ics files (make sure that no duplicates are created when importing - not every calendar app prevents duplicates).
The best calendar app of all time for Android is CalenGoo.
Despite the name, it can also be used offline without Google and offers everything your heart desires. Even recurring appointments can be created within seconds thanks to easy template creation.
I have used this app for many years.
Messages: If you mean chats made on messengers:
Good messenger services have apps with their own local export + import possibility.
The best tech solution has SimpleX Chat, which can export and import its database with the chats also as the design theme for the whole app and separate also the theme of every chat room, if you have chosen separate designs for each chat partner or chat group.
SimpleX is platform-independent and can be quickly moved between iOS and Android/GOS devices at any time, along with the backups. No chat history is lost due to a change of device.
If you mean text messages (SMS):
The stock SMS app delivered with GrapheneOS cannot import your SMS, but there are other SMS apps with the possibility to export and import SMS messages.
If you install an alternative SMS app on GOS, you can make it to the standard app for SMS.