How do I backup messages on an Apple iPhone?

Use iCloud to backup and sync your imessages and texts / SMS on your Apple devices

Warning: When signing in with an Apple ID, do not use a personal one. Instead request a diocesan work Apple ID by raising a support ticket.

Set up iCloud for Messages on all your devices

See https://support.apple.com/en-gb/guide/icloud/mm0de0d4528d/1.0/icloud/1.0