I've been taking a further ook through the 1891/1901/1911census records, and nothing is standing out. That said, Elizabeth and William Davies are rather common names. There is no Elizabeth Davies b. 1888-1892 in Sunderland in the bdm indexes.
What more details do you have about the Russian story? Any potential names of siblings, dates, was her mother supposed to have been Russian, or were they an Enlgish family there for William's engineering work?
I see you've taken a DNA test. Have you looked at the Leeds method? This will help you cluster your DNA matches and hopefully isolate those related to you onthe Davies line which could give you further clues as to Elizabeth's parents