I accidentally deleted the Google search app. How can I restore or reinstall the app?

There’s no “magic trick”. You deleted an App that is no longer available.

You shouldn’t be too disheartened. The so-called “App” is only a web front-end that allows Google to scrape/log even more information about you, your habits - and your data.

You are now relegated to using Google search in a Web browser now.

Google no longer supports iOS versions older than iOS/iPadOS13 - and have withdrawn older versions from the App Store. Having deleted the working (older) App from your iPad, you cannot now reinstall the App.

A first generation iPad Air, iPad mini2 and mini3 can only be updated to iOS 12.5.3. With iOS 12.5.3 installed, you will have one of these three models.

Apple ended major update support for these models of iPad in September 2019 - although they since continue to receive “point” security updates. These devices cannot be updated to iPadOS 13 (or any later major versions of iPadOS) as the internal hardware does not meet the minimum technical requirements (CPU and RAM) for newer versions of iOS/iPadOS.

Some App developers, such as Google, comments have dropped support for iOS versions preceding iOS 13.x for technical reasons (often because APIs or software libraries upon which they rely have been updated in the new version of iPadOS, making their App incompatible with earlier versions). 

Whilst many App titles remain compatible with your iPad, if you want or need to access to Apps requiring the most recent versions of iOS, you’ll need to consider replacement of your iPad with a newer or current model that supports iPadOS14.

Sorry, I appreciate that this may not be what you were hoping to learn.

As the error message says, the app is available only for iOS 13 or higher.

Try contacting Google Support and see if they can provide you the version available for your current iOS.