I can't see the pics either as others have mentioned. So can't say using a pressure washer is a good idea since we don't know your basement setup.

But try deep cleaning it as another suggested. Why don't you also get a air purifier to help filter out the particulates in the room too? It'd probably be a good thing since the "fresh air" from outside is also a byproduct of the nearby wildfires. So filtering out some of that inside your entire house might be a good thing.

Also you might want to check your HVAC filter and change it more often as it might be more dirty/clogged from the brick dust.