some activities require a proof of residency AND salary in Japan
The kinds of activities someone does while travelling for 3-6 months?
I believe renting somewhere to live often does, so yes.
If you rent for short term (6 months), monthly mansions don't need bank accounts or proof of residency. It costs about 50% more than you'd pay for long term but you don't have to pay reikin (key money you don't get back), shikikin (deposit for damages).
it may be cheaper to live in a hostel rather than a monthly mansion, but depends on your tastes
Like what activities?
gym membership, certain ride share bike rentals in some cities. just few things I tried to do during my last trip.