The context menus of the editor are mostly dependent on the used HTML markup.
As you surely have realized is that they are configured for each desired tag and show up accordingly the selected element (tag name).
In cases of pasted content, you can examine what exactly is pasted and how is generated as HTML markup and see if the tags are as configured. If not, I can suggest reconfigure the context menus according the encountered cases.
Also, I suggest posting a sample code or attach a simple project, so that it could be examined locally and investigated properly. Without exact details about the built code, I can only make assumptions on the exact scenario.
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