How can I retrieve text messages from an old broken iPhone

If you were syncing Messages with iCloud, turn Messages syncing on after logging into Settings/Your Name using the same Apple ID.

If you weren't syncing Messages to iCloud, o you have a backup you can restore from? Restoring from a backup erases all data currently on your device. Any data newer then when the backup was made will be erased. A restore is an all or nothing restore. You can't access a backup to see the contents and only restore certain files.

 Backups - Locate backups of your iPhone, iPad, and iPod touch.   *

Backup - Restore your device from an iCloud or iTunes backup.    *

ASC YouTube for how to restore an iPhone, iPad, or iPod touch from an iCloud backup