Apple watch app

If it says "Open" that means the app is installed on your phone.

Start here:

Organize the Home Screen and App Library on your iPhone - Apple Support

Once you find the app in the App Library, you can touch and hold on it and then tap the "Add to Home Screen" option.

If you can't find it there, check Settings>Screen Time to see if it has been restricted.

For future reference.

If you put your finger in the middle of the screen (NOT on any icon) and pull down, you will get a search box at the top of the screen where you can type in "Watch" and it will find the app.

You can launch the app from the search display if you like.

If the found app is in a folder, the folder name will be displayed to the right of the app name. In the screenshot below, I have my "Watch" app stored in my Health folder. If there is no folder name on the right side, then the app is on one of your app screens. And you can then match the icon shown by the search results against the app icons on the different screens.

If it says open then it is on your phone,swipe all the way to the left on your phone and you should see the watch app in your phone's app library.

Glad it helped!