Hi iHaveBadAlias,
Thanks for getting back to us with the additional information. I would like to have you try the following next, testing if you're only seeing a partial keyboard in the App Store after each step:
- Force the App Store to close: How to force an app to close on your iPhone, iPad, or iPod touch - Apple Support
- Restart your iPhone: Restart your iPhone, iPad, or iPod touch - Apple Support
- Isolate if there are any potential hardware issues with your display following the steps here: Get help with the display on your iPhone, iPad, or iPod touch - Apple Support
If you're still encountering the behavior after trying those steps, I would like to have you go to Settings > General > Reset > Reset All Settings. This will revert any settings that you've customized or changed on your iPhone so you may need to reconfigure some of those settings again afterwards:
Return iPhone settings to their defaults - Apple Support
- "Reset All Settings: All settings—including network settings, the keyboard dictionary, the Home screen layout, location settings, privacy settings, and Apple Pay cards—are removed or reset to their defaults. No data or media are deleted."
While you won't lose data in the process, it is always a good idea to make sure you have a backup of your device first:
How to back up your iPhone, iPad, and iPod touch - Apple Support
Keep us posted on the results.
Take care.