I made a simpler test page at https://en.wikipedia.org/wiki/User:PrimeHunter/VisualEditor_note_duplication

Now I added another note with same group name outside of the infobox. When I switch to VisualEdit mode, this time the note outside of infobox disappears

I don't see that happening on the original page you mentioned (it has two identical notes in read mode, one of which vanishes when you launch VE because it's defined inside a template, but no further use of Cite causes any duplication), but I see the persistent duplications happening in your simpler example.

Given that the example is:

{{Infobox scientist
| awards = Peace Prize<ref group="n">Note</ref>
}}
Edit this page in VisualEditor and click the Cite button. The note display is duplicated or more.

== Notes ==
<references group="n"></references>

...I'd suspect it's related to the template-defined reference.

Here's a video of it happening: https://youtu.be/-P63pkat4Bo