For me (as you suggest in intro) it doesn't replace the current plugin for quickly adding inline citations - the lag feels really long, and I was often second guessing whether it was being added or not.
It would be nice if it recognised the current citation style already being used. I tried it on a current doc and it inserted in a completely different style.
I can see it being really useful from the point of view of having all current ref's easily accessible. I often want to remind myself about an article text, so having it one click away is nice - it would be great if as well as the "Edit | Website" options there was "Open PDF in paperpile" or similar option to quickly bring up the PDF if it exists - this could work great with the PDF annotation app.
Similar to @florian above, the behavior with hover on a citation feels a bit incomplete. I think identifying it with the "blue tag" is great, but it would be good if the list changed focus to the article(s) to facilitate (for eg) rapidly clicking on it to see the pdf etc etc - or perhaps the "Blue tag" could be more useful (rather than just allowing some minor citation edits) and clicking on it would focus to the article in the list above or present an option to click through to the website/pdf etc. At present, you have to scroll through to find the green check mark.
At the moment, clicking anywhere in individual citation "box" immediately adds it as a citation and one has to click on the small ellipsis to expand the "options". It would feel cleaner to me to have to click on the " or a check mark to add it as a citation (making it very explicit) with clicking "anywhere" expanding the options?
I guess all my comments are trying to make a "citation manager" do more than that, and act a bit more like a research/article manager? I'm not sure if that's what your looking at doing, but it felt like it could easily turn in to that (which would be great!).
Thanks for all your great work - paperpile is fantastic.