The Moon landing sites have been photographed, but from orbit around the Moon. For example: https://www.nasa.gov/mission_pages/LRO/news/apollo-sites.html It is legitimate to ask why not from the Earth?
A lunar module has a diameter of about 4m. At a distance of 400,000 km, this subtends an angle of 0.002 arcseconds.
The absolute best angular resolution you can obtain from the surface of the Earth, using massive telescopes and adaptive optics imaging is about 0.1 arcsecond.
i.e. You cannot resolve anything on the Moon's surface, using a telescope on Earth, that is much smaller than about 200 m in diameter.
The observations you refer to (see Wang et al. 2020) are of a galaxy, taken at microwave wavelengths (so hardly comparable). A galaxy is far away, but very big. The observations were able to resolve emission from the central 20 kpc (about 60 thousand light years) diameter region of this galaxy. The galaxy itself is at a distance of about 180 Mpc (about 600 million light years), so the angular resolution involved, using a bit of basic trigonometry, was about 22 arcseconds, which is set by the instrumentation they were using (i.e. the signature they found could be more concentrated than that). Thus this central region in Markarian 231 subtends an angle of 22 arcseconds at the Earth, which is roughly 10,000 times the apparent size of a lunar module on the surface of the Moon.