How do I download widget from App Store if it just shows open instead of get

If it still shows 'Open', you did not actually delete it from your phone. It is still on your phone. What you did is 'Remove' it from your Home Screen, which is not the same as deleting.

For further verification, you should be able to go to Settings and find this app name listed.

To open or access the app, as you saw in the App Store, you can just press Open from there.

Or from any Home Screen, you can swipe downward to access the search feature. Here you can type the name of the app and it should show up.

Or to access the App Library, you would swipe left on your Home Screen until you get to the very last screen, which should show all your apps grouped into pre-defined categories.. With a search field up top that says App Library. You can dig around in those pre-defined categories, but I find it easier to use the search field, or swipe downward and you'll get an alphabetical list of all the apps that are on your phone.

Once located, if you want to move it to your Home Screen, just tap/hold then drag it.

All of this is assuming that you are running iOS 14 or later, when Home Screen widgets were introduced along with that App Library. Then iOS 16 introduces widgets on the Lock Screen.

Previously, I believe the only 'widgets' that existed would have been in Today View.. which is if you swipe right to the farthest screen.

You don't download widgets from the App Store, you download apps.

The app might allow you to add or create widgets..

If the App Store shows 'Open' rather than 'Get', then the app is already installed on your phone.

You can find the app using the search function or the App Library

As I commented in my prior response.. when you locate the app in the App Library via search or scrolling thru the alphabetical list.. tap/hold and then drag the app name, it’ll pop out to your Home Screen

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