Astronomers can now measure distance to stars directly with parallax surveying, so the question of whether stars are more than 10,000 light years away is solved. They should be able to measure out to at least 50,000 light years with the current satellite.
I may be mistaken in the details, but by using aperture synthesis, radio astronomers can take signals at point A, then take signals six months later at point B when the earth is on the opposite side of the sun, and combine the two, it is like having a dish antenna as big as the distance from A to B.
Baby, that’s some parallax.