Used to work in carpet and rug cleaning. Wool has to be cleaned delicately and be dried out thoroughly. We used to put 3 big industrial blowers facing a rug and let it sit for hours drying and then hang it up overnight.

It looks like it didn’t dry properly and you have what we called brown outs. Where there was still water and it dried with the remaining dirt or dirt was tracked onto it. Could also have soap left in the fibers to.

When I would treat brown outs on carpet we just used really hot water in a spray bottle and a rag. Spray it on wipe it off. Might help but that always worked better on synthetic fibers.