I appreciate the detailed information about your concern and the steps you've performed to resolve the screen issues, @schmalts. I'll share the direct link to download the QBO Desktop App.
Downloading the QuickBooks Online (QBO) desktop app via the Gear icon is only available on QBO Advanced and Accountant versions. Also, it needs a Windows 64-bit processor in your software to have the feature.
Below are the links you can use to download the app. Before that, let's ensure you have a 64-bit processor if you're using a Windows computer. Once ready, refer to the links below:
Additionally, to easily access your QBO app, you can add a shortcut or icon to your desktop. For detailed steps, check out this article: Create a desktop shortcut for QuickBooks Online.
I'm ready to back you up if you need more help downloading and installing QuickBooks products or any concerns you may have. I'm always here to help. Stay safe.