Partner 3 is a Mii from the 3DS.
Partner 3 originally appeared as one of four sample Miis used in the 3DS debug application FriendTestingPartner found in the September 2020 Nintendo leak. She hasn't appeared in any game. She can be found in the main.cpp file, with the hexadecimal of her Mii data file simply printed as text embedded in the code of the file.
She was originally made on a 3DS (3), her Mii name in her Mii data file is Partner 3, has Copying turned on, and Sharing turned on. Her Mii ID is 90-F1-98-B3. Her Mii ID tells us she was created on January 2nd, 2011, 12:18:44 PM.
Her Mii data file contains unused data. Her mouth color is set to the 3rd option. Her facial hair color is set to the 7th option.
Partner 3 only appears in the debug 3DS application FriendTestingPartner. Once ran, the user who ran it will now appear differently in the Friend List. The user Mii will cycle through Partners 1, 2, 3, and 4 in order. The "currently playing" will also cycle through multiple applications in a random order (the applications it can choose from is listed below). The status displayed is a timestamp of when the Mii was switched, using just numbers. A screenshot of the Friend List after someone else is running the FriendTestingPartner application (specifically when the Mii shown is Partner 3) can be found in the image appearances section of Partner 3's page.
Partner 3 unfortunately does not appear in any promo art. Here is a screenshot of a 3DS's Friend List after one of the people in my friends list run the FriendTestingPartner application. The screenshot is of someone else running the application, as if I was the one running the application, I could not properly take screenshots of the Friends List while it's in action.
Note some black rectangles in the screenshot: this was edited in by myself to protect the privacy of the people on my Friends List. It has no relevance to the debug application or the Miis.
Also note that the timestamps in the status message at the top screen are different - this is because the status message takes an extra second to update, and this screenshot was taken before it fully updated to match the top screen's. Under normal circumstances, it should match.