Pasting an image from, say, Google Docs, and many other sources, works. The TinyMCE adds the appropriate <img src="data:…">.
Pasting from Word works when using the PowerPaste plugin, which is commercial.
There is an open source plugin, tinymce-paste-from-word-plugin, but pasting an image from Word didn't work for me even after installing and enabling the plugin. It is unclear to me whether this is supposed to work when using that plugin, but I've opened #125 on the relevant project.
Us not being able to move to TinyMCE 7 is a big motivation to look at other options (see #4632), and it could also be chance to pick one that supports this features out-of-the-box.
To reproduce, open cat.docx in Word, copy, and paste in a formatted text area.
It works with Safari, but not with Chrome and Firefox.
With Chrome, the console error is: Not allowed to load local resource: file:///Users/avernet/Library/Group%20Containers/UBF8T346G9.Office/TemporaryItems/msohtmlclip/clip_image001.jpg
<img src="data:…">
.