Hi Mark,
Your expectations are valid and you should be able to group layout text element for ease of use. Currently, I'm unaware of any known issues concerning the grouping/ungrouping of text elements in a Layout View. From the screenshot you provided I don't see any element that is turned on in the Contents pane, yet I see text displaying on the Layout View (page). These text elements don't seem to correspond to any item in the Contents pane. They seem to be in a bad state - one in which I doubt you'll be able to recover the text much less edit.
I'd be very interested in how the text elements got into this state, but as Thomas stated above, we need steps/data to reproduce the problem. Can you contact Esri Support? They are better equipped to handle troubleshooting steps and gather bug data. They can be contacted at https://support.esri.com/en/contact-tech-support.
In the meantime, try copy/pasting the layout in the same project, or saving the project out as a new project. This MIGHT reset the layout and either remove the bad element. Also, I'm assuming that the text is labeling features/areas of your map. Is there any reason that you are not using labeling or annotation?
Here are some links to annotation and labeling help topics:
Annotation—ArcGIS Pro | ArcGIS Desktop
Create annotation feature classes—ArcGIS Pro | ArcGIS Desktop
Labeling basics—ArcGIS Pro | ArcGIS Desktop
Hope this helps,
Tom