At last I decided to give a try to Firefly III, set up server, installed client, aaaaaaaand mobile app doesn't work :D
Met github.com/victorbalssa/abacus right from the start.

Very common thing for OSS: everything works perfectly for decades if you ask a long-term user but it's always not the right time for newcomer to join :)

Nevertheless the system looks promising and it seems that just sharing credentials will do for shared budget.