Interesting. I have a few thoughts.
Rare earth elements are currently sourced essentially from two distinct mineralogies: hard rock mining from igneous intrusions with the rare earths contained in e.g. bastnaesite and monazite (such as Bayan Obo in Inner Mongolia and Mountain Pass in California), and from ion absorption clays (for reasons above my pay grade these only occur in the subtropical belts hence their prevalence in southern China).
These two ores have some important distinguishing characteristics. Firstly, the hard rock ores tend to be enriched in the so-called "light" REEs (e.g. lanthanum, cerium) whereas the clays are somewhat enriched in the "heavy" REEs (e.g. lutetium, yttrium). They also have very different processing methods. Hard rock ores are processed in a more conventional way, via grinding/milling the ore, floating the valuables and then sequentially removing elements using solvent extraction. With maybe leaching in there somewhere... This is more or less similar to processing for the precious metals but as I understand it the large number and chemical similarity of the REEs makes this more resource intensive. On the other hand, in the clay ores the REEs are already in the free ionic form and are flushed out via ion exchange in heaps or vats.
Both of these processing methods are pretty nasty but one falls under the remit of large state-controlled enterprise and the other can be done by a dude with a spade and a vat full of salt water. So it's no surprise that there is a large unregulated industry around the processing of these clays, which is in turn responsible for some seriously hellish mining landscapes and environmental degradation. The Chinese government is apparently cracking down on that sort of thing which I can only imagine involves a lot of authoritarian police state tactics.
Coming back to the article, I wasn't entirely sure at what part of the above processes this advancement would fit in. The paper they are referecing seems to have used spent ceria polishing powder and lutetium crystal waste as the feedstock for their experiments (i.e. already very pure in terms of REE content). So it appears that this applies to the extraction phase - they first had to go through an alkaline roast and HCl dissolution before using the new solvent. This doesn't really enable making a big difference to the overall production process. In the conventional mining case, it will still need to produce masses of somewhat radioactive tailings, require massive amounts of energy to grind the ore and so on. Similar situation for the clay mining. It's an unfortunate reality that the amount of value added in a processing step tends to be inversely proportional to the environmental impact associated, and this technology seems to be acting on the end of the pipe.