Yes, there are programs that can extract the SMS file from your backup.
http://www.backuptrans.com/iphone-sms-transfer.html
Are you asking if there's an officially sanctioned, built-in, way?
I am not sure why you are reluctant to not having another application which can manage your texts, but I would personally recommend Text Saver from MyPhoneData as I have used it and liked every bit about it.
See, if Apple does not allow you to take backups of your text message (or other data), there needs to be a reliance on 3rd party apps which can do the same for us.
Hope this helps.
I thought you could back up text messages via iCloud? Am I wrong?
I use to use this publisher's DiskAid and it worked great. But then their meal ticket was to not support future iOS version and instead simply reinvent their own wheel by changing the product name for the newer iOS versions. That basically meant previous owners had to buy again.I use iMazing for everything. It has some great SMS features:
https://imazing.com/features/transfer-iphone-text-messages-to-computer
Not free ($40), but there are usually some coupons floating around if you look.