Hi,
Right now it is possible to export your contacts to .vcf file and there’s no way to export your messages to the file. If you want to backup your messages you can perform a phone backup, which will back up your messages as well - you can then restore the backup and take a look at your messages.
I’ll pass the idea of exporting the messages to the file further - it does sound like a cool feature.
Is it possible to have the feature to back up call logs & SMS messages in a file format? That would be an incredibly helpful feature to add in the future!