Given all the uses of compressed gas, I find it difficult to imagine that a pressurized cylinder is illegal in a residence. Does that mean no propane, no CO2 for beverages, no medical O2, etc?
There must be a way to get a tank of breathing air in one of the world's largest cities. It's an absolute necessity for self servicing regulators. It's similar to trying to service electronic equipment without a power source. The tank rental idea will be prohibitively expensive if you plan on checking and servicing your own regs regularly, so it would be best to buy something from the start.
You mentioned you're taking a class so that you can 'take care of basics' at home. Would you elaborate on that? Typically the so-called regulator maintenance classes offered by the big training agencies are not much more than "rinse, check IP, and go to your dealer for service" sorts of classes. If you are taking one of those, I would suggest it's probably a waste of money, (the information they offer is freely available) but the upside is that you would not need to find a tank.
You'd be surprised, shocked even at the number of laws and rules we have to put up with here that would be considered absurd in the western world, a lot of it centered around ultra-conservative safety in a densely populated area but also quite a bit of them are also about removing the possibility of inconveniencing or annoying your neighbors (no kidding!). To your examples, propane (in any sizable tank) in the city these days is a definite no-no, CO2 is a commercial application so that's a different story, medical uses like O2 are exempted generally. Any vehicle carrying bottles of compressed gas have to put a giant warning sticker on the front and rear but funnily taxis do not, though Tokyo taxis have been using CNG for years.
Japan is not a DIY culture country, they nearly always call in the so-called "professional" for what we'd consider to be very simple repairs and maintenance, whether that be in the home, on the car, SCUBA gear, etc.. So the government of Tokyo prefecture doesn't care about a few foreign divers who want to service their own gear, the compressed gas laws weren't put into place with that in consideration. Similarly annoying to divers, we also have very strict knife laws, so if you're carrying any knife over 6cm then it needs to be for an obvious purpose (like fishing, diving, etc. and accompanied by appropriate sport gear) or you'll land a quick trip to a detention center.
I did inquire with one of the local tech diver instructors (foreigner), he said around here, there's one dive location about 200km away that will fill private tanks that are Japan certified (so no imported tanks) and there's a SCUBA club at Yokosuka Navy Base (about 60km away) that has a compressor to fill tanks, but you have to have base access to use it.
I knew Japanese divers almost never own tanks, but didn't realize until recently that it's such a royal PITA for those who really want to.
Agree, I think some courses are probably light in content. I want to make sure I'm taking something that teaches me to do my own OHs safely and confidently. I can get OH kits at reasonable prices, but labor cost here is very high, and it takes the shop 2 weeks to get it back to me. The class I'm looking at is done by a Tech diver, he says it's a thorough class but it's not under any certification agency. They teach using Apeks, an OH of 1st & 2nd stage in the class and provide OH kits for Apeks and other brands they can source. (I have one Apeks set and one Atomic set, he says he can't get Atomic parts but I can get them myself).
I think the only solution is going to be to get a Japanese spec deco tank. There's only one shop who even advertises them on the internet, they aren't terribly unreasonable for the tank but opportunities to fill are so limited. Shockingly a decent size deco tank is hardly any more expensive than a 1-2.5L Pony.