I have arcgis pro 2.7.1 and sde.
Please see screenshot and advise. It is sde feature class. Thank you for your assistance.
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I found out I have other application open with same data and data network has been disconnected. I had to close it.
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160557: The object cannot be edited using the current edit session mode.—ArcGIS Pro | Documentation
quit editing, stop the program, reboot the computer ... not the solution I suppose, but you didn't indicate what you tried