Sorry to say but sealing the gaps sounds to be the immediate solution for "your side" of the garage. If he is intent on using the space for his chosen trade, then your neighbour urgently needs to equip his garage with a cyclone (something like this:
https://youtu.be/3ni1Pf-wwo0). Especially as stone dust is so much more noxious than wood dust. Cyclones are also used in animal feedstuff production facilities
https://www.aairex.com/animal-feed-production-dust-extraction-system/I worked for years in the textile industry and visited mills around the world, some of which were seriously life-threatening on many levels, especially festoons of airborne cotton fibres (known as "fly") hanging from the roof and various ducting. I survived, but I knew a number of industry professionals who succumbed to horrible diseases like byssinosis, don't let it happen to you (even as a "passive" inhaler). I would also get your local Environmental Health involved right away to monitor dust levels (and, I'm guessing, noise). If he complains, tell him that if he's not causing a statutory nuisance, he has nothing to fear.
