Has the Earth's wobble around the Earth-Moon barycenter ever been observed by a spacecraft?
Absolutely yes if you can count the wobbling motion of the spacecraft that tracks Earth's wobble about the Earth-Moon barycenter.
DSCOVR sits in a heliocentric orbit which is in a 1:1 resonance with Earth, otherwise known as a "Lissajous orbit associated with Sun-Earth L1".
Its EPIC camera is pointed carefully at Earth all the time in order to keep a 0.45° to 0.53° Earth nicely framed in its only slightly larger 0.61° field of view.
If the Earth-Moon average distance is 385,000 km and they have a mass ratio of 81:1, Earth's wobble should be roughly 4,800 km or about 38% of its diameter. If DSCOVR didn't track this wobble the Earth would appear to move +/- 0.18° in EPIC's field of view such that parts of Earth would disappear outside the frame around the times of first and third quarter of the Moon as seen from Earth.
One can download roughly daily data dumps from EPIC which contain data fields for the pointing vectors of the camera. One can subtract a smoothly varying rotation of $2 \pi$ per year and see both Earth's eccentricity and a monthly wobble due to center-of-mass motion of the Earth. I've looked at EPIC metadata in the past, and while I haven't done this specific analysis this can't not be true!
From this answer:
above: Image from NASA/NOAA from Bad Astronomy