If you've already purchased an app and can't find it in the App Store, you may need to sign out of the Apple ID you're currently using and sign in with the Apple ID that you purchased the app or game with. On iOS 15 and iPadOS 15, you can easily redownload apps that you've previously purchased from your Apple ID account in the App Store itself. To redownload an app, open the App Store and tap on your profile icon in the top right corner. Then, tap on Purchased.
Here, you'll see a list of all the apps and games that you've ever purchased with your Apple ID. Tap on the one you want to redownload and then tap on Download. If you're having trouble finding an app that you know you've purchased, try searching for it in the App Store. Tap on the magnifying glass icon in the bottom right corner and type in the name of the app.
If it's available for download, it should appear in your search results. If you still can't find an app that you know you've purchased, try restarting your device or signing out of your Apple ID and signing back in. This should help refresh your account and make any apps that are available for download appear in your Purchased list. If none of these steps work, unfortunately, there's not much else you can do.
You may need to purchase the app again if it's no longer available for download.