When using Obsidian & Paperpile for my Master’s, I found the best approach was to insert the cite key for the paper in my writing, where the full in-line citation would usually go. I put these into square brackets, as I’d use that linked note for my general dumping of highlights, thoughts, and such after reading and annotating.
That way, the annotation locations were easy enough to spot once I was ready for pasting over to Word. It was then a matter of double-clicking the in-line cite key, Ctrl+C to copy it, hitting the keyboard shortcut for the Paperpile Word plugin, and pasting the cite key into the paper search box to bring up the correct paper to reference in that location.
Not the slickest method, and it would be lovely if the plugin scanned through the text for all of the cite keys and did an automatic replacement, but that process just became part of my final read-through and auditing.
In the end, I sucked it up and learned to use LaTeX, partly because Word’s implementation of equations was making me very angry… The Bibtex reference worked from the citekey, and it became second nature to type /autocite{citekey} while in the writing flow.
As an aside, that workflow was similar to mine except I downloaded the .md export of highlights and imported it into Obsidian. There seems to be some difference between the Markdown generated in the browser, and for the download. The latter kept more useful formatting, for me personally.