Even the Onenote icon on the start menu that had '2016' next to it no longer has the 2016. In any case, as soon as I completely uninstalled Office 2010 from Control Panel, all of my Word files magically had the 2019 icons and nothing further such as uninstalling 2019 was necessary. I wanted to keep some of the 2010 programs that are not included in 2019 and I had already uninstalled Word and Excel 2010 (unless it really just hides them. I had thought of uninstalling as an absolute last resort. I suggest using the Microsoft Office Uninstall Tool - see Steve! I cannot thank you enough after this has driven me crazy for over a week, maybe even two weeks.

I suggest uninstalling all versions of Office and reinstalling Office 2019 again. Have you tried a repair install of Office 2019? It's normally good practise to uninstall an old version of Office before installing the new one.