Hey Principessa66,
Welcome to Apple Support Communities.
You've gone through some great troubleshooting steps. We suggest attempting to download another app. This will determine whether the issue is only with the Keynote app or system wide.
If the issue is system wide and you're using cellular data, try a Wi-Fi network. If the issue is with a Wi-Fi network, try with cellular data or different Wi-Fi networks. Trying a different network will ensure the issue isn't specific to just the one.
If you're able to download the app using a different network, reach out to your internet service provider or wireless carrier for assistance with the network that isn't working as expected.
The latest iPadOS version is 16.5.1. Check Settings > General About, to confirm it's up-to-date. If not, follow the steps below to update and then try installing the Keynote app again.
Go to Settings 
> General > Software Update.
The screen shows the currently installed version of iPadOS and whether an update is available.
To turn off automatic updates, go to Settings > General > Software Update > Automatic Updates.
You can also locate the steps here: Update iPadOS. If you run into issues updating wirelessly, the article provides steps to update using a computer.
If the steps above do not help, we recommending contacting Apple Support here: Get Support. They will be able to further assist you.
Best wishes.
