IPhoto missing

If you are saying that Photos (with the multi-colored flower icon that Old Toad shared) is not found on your Mac, you have issues since it is a system program and has nothing to do with the App store.

Try a spotlight search for Photos - or what the equivalent might be in your language. If it is not there, your update to Catalina did not go correctly, and you should install the latest combo-updater:

https://support.apple.com/kb/DL2048?locale=en_US

Priscilla, your screenshot in this post is showing that the Photos.app is running: https://discussions.apple.com/thread/251609765?answerId=253112341022#253112341022

The "Choose Library" dialog is displayed by the Photos.app, when it is running. So the Photos.app is installed. It is a part of the system. What is missing is the Photos Library or the iPhoto Library. Your Photos are stored by the iPhoto application or Photos application, but not inside the the application. They are stored in a separate database, called iPhoto Library or Photos Library (if you did not rename them) and will by default be in your Pictures folder. Reinstalling an application will just refresh the program, not bring your your photos back, They are stored separately. Have you searched for your iPhoto Library as Keith Barkley recommended?

You need to find an item with a fan of three pictures with a flower. The icon of the iPhoto Library will show a pink flower:

And the Photos Library will show a rainbow flower:

Are you seeing any items like this in your Pictures folder or Documents, on your Desktop? Anywhere in your Home folder or on connected backup drives?

To search systematically,

• open a Finder winder and enter the key combination ⌘F to open a search window.
• Now enter "photolibrary" into the search field and click the suggestion "Kind: Photo Library".
• Make sure, the search scope is set to "This Mac".

Does this find any libraries?

iPhoto was discontinued several years ago and replace by Photos:

It should be in the Dock and Applications folder. Drag your iPhoto library onto the Photos icon and it will be migrated to a new Photos library.

If you haven't access the photo app in a couple of years, you may have your old iPhoto.library sitting on your laptop, but iPhoto was retired a couple of years ago and replace by the Photos app. Launching Photos, it may see your old iPhoto library and ask you if you want to use it. Alternatively, you can locate your iPhotos library via Finder and double-click it to launch, then select Photos as the application to use for it. If given the option to convert your old library over to a Photos library, definitely do that. Once you're confident that everything has been transferred into Photos, and that you have a photos.library on your laptop, you can delete the old iPhotos.library file.

Photos is on your computer our you would not be getting the dialogs you have been sharing in your screenshots, since those come from Photos. (See the multicolored flower in the dialog?) If you have your computer's language set to something other than english, Photos might be called its equivalent in your language.

Photos is the app that manages your libraries and images. The images are actually stored in a file usually called something like Photos Library.photoslibrary

The question is whether your library is on the computer. Can you show us a screenshot of the contents of your picture's folder?

I don't see how it could be missing as it's part of the System can can't be deleted.

Download and apply the macOS Catalina 10.15.6 Combo Update.  It will include the latest Photos app.

Perfect, select "open other" and point it to your iPhoto Library.

Where was your iPhoto Library? Was it on an external disk?

Try entering "iPhoto Library" in the search bar at the top of the Mac.