On the bright side, I don't have to write a repro code sample for this issue since this is present in the example on https://www.telerik.com/blazor-ui/documentation/components/grid/templates/popup-form-template#example
The popup for adding a new item now shows the values of the previously edited item. The same goes for editing any other item. As long as the popup is closed with the "x" in the top right, the edit context remains.
The Problem relates to the ExitGridEditMode method and when it is and isn't called. Specifically, it is not called when the edit popup is closed with the close button in the top right of the window. I have also not found any way to get notified about the edit popup being closed with the close button. The Grid contains a hard-coded <TelerikWindow> and there doesn't appear to be a way to influence this window action or any events that it triggers.