Tap Settings on the Home Screen
Tap on your name at the top of the next screen
Tap iCloud
Tap iCloud Backup
The time of the last backup should appear
Backups occur about every 24 hours as long as the iPhone is connected to the network and the charger. It is not possible to know in advance exactly when the next backup will run.
You can also back up manually at any time by selecting Back Up Now
There is another possible fly in the ointment and that is the iCloud settings for Messages. In order for Messages to back up to iCloud, the setting must be "Off" when you check as follows:
Settings > iCloud
This will display options to back up or not back up a number of items. It might seem unintuitive, but the slider must be "Off" next to Messages in order for Messages to be backed up to iCloud. If the setting for Messages is "On", then Messages are not being backed up to iCloud.
Even if you find that the Messages you want are still in the iCloud backup, things are messy. You have to reset/erase the iPhone and then use the backup to restore. So, you will lose any new data that you have added to the iPhone since the time of the backup.
The bottom line......don't delete any message unless you are sure that you will never need it again in the future.