messages on iPhone

If you are missing the red badge on your message icon, first check if it is activated here:

Settings → Notifications → Messages → Badges must be enabled.

If Badges is enabled, check if you have Do Not Disturb or any of the other Focus profiles enabled, eg Sleep. If you have, you can deactivate the profile in the Control Center. Do Not Disturb hides App Badges when enabled.

Pull the Control Center down from the top right corner. Find the Focus Button, just below Screen Rotate Lock and Screen Mirror, tap and deactivate the active profile.

If Do Not Disturb or another Focus profile activates automatically, then a Schedule is active.

To disable or delete this schedule, go to:

Settings → Focus → Select Profile → find SET A SCHEDULE → Tap into the time → tap Delete Schedule or just deactivate.

You can read more about how to use Focus here:

Use Focus on your iPhone or iPad - Apple Support