iPhone 13 not making text notification sound

That is working the way it is supposed to. With the Apple Watch, notifications work a specific way. See this for how notifications work with the Apple Watch. Notifications on your Apple Watch - Apple Support

No. The way it works is by design and exactly as Apple chose the notification path. If your iPhone is open, meaning you are using it, you'll get notifications on your iPhone. If the screen is locked and you have Apple Watch on your wrist, you get notifications on your watch.

The initial purpose of the Watch was more as a notification device, so you did not have to take the phone out of your pocket/purse, and you would receive notifications and be able to view them.

You have the option to provide feedback to Apple if you would like to see a change at Feedback - Apple Watch - Apple but it has been this way since the beginning so I'm not sure you will see it happen.

This is becuase your watch got the notification and ether told you or your watch is in silent mode. If it’s in silent mode, you don’t get a sound from your devices. If it’s off then you should get a “ding” from your watch

kwayne wrote:

I appreciate you taking time to help me with my situation. But I am letting you know for several years now my phone has been giving sound and vibration along with the watch. I have worn the watch and carried the phone every day together during that time. It is Only since the upgrade to 13pro and watch update that I do not get both. Maybe it has been a fluke but they need to make it a option.

That is unusual in that its not supposed to work that way. I've been wearing Apple Watch since Series 3 was introduced (then 4 and now 7) and have never had both phone and watch make sounds at the same time for notifications. And as can be seen in the Apple Support document provided above about notifications, that is how its designed to work.

Like lobsterghost1, I've had the Apple Watches for a long time. Actually I purchased an original, and have had one of every series since then, and still have my Series 6. I don't see enough of a change to get the Series 7. I also change phones annually through the iPhone Upgrade Program. I can tell you that my Watch & Phone have never had the phone and Watch sound notifications together. If yours was doing that, it was an anomaly. It is working just the way it is supposed to now.