If I understand your issue correctly you are saying that you are trying to insert a picture element onto a layout and you do not see the Graphics group (circled in red below) in the Insert tab of the ribbon.
Is this correct?
I customized the ribbon and added the Graphics tab to the Insert tab so I could insert pictures. But adding pictures doesn’t work. A Blueish box appears in the lower left and I am unable to drag a rectangle to add the picture.
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Which view are you trying to add a picture to? Layout? Map?
If it is to a Layout View why do you need to add the Graphics Group to the ribbon since it should already be there, if it was not manually removed through customization. If for some reason the Picture button, or the entire Graphics group, is missing from the Insert tab with an active layout this may be a bug and should be reported to 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.
If you added the insert Picture to the Map View... this is not supported. To show pictures on the map (in geographic space) you will need to create a point feature class. Create point in the map location where you want the picture to appear and symbolize the point with picture marker symbol (see Marker symbol layers—ArcGIS Pro | ArcGIS Desktop).
For more information on working with graphics (including pictures) in the Layout View please refer to Add and modify graphics and text—Layouts | ArcGIS Desktop .