If you're in a taxi and there's no seatbelts, you're definitely in a wrong kind of taxi. Better not board anything like that.
This is after we exclude small remote towns where it's still not uncommon. As a rule you can expect taxi car to be in reasonable condition, and this includes seat belts for all passengers.
Sometimes for the seats in a back, seat belts may not be easily accessible. You will have to dig them out of the seat, or just ride in the front seat. It's a preferred option in Russia anyway.
Obviously if you're unhappy about your taxi and you hailed it via app or phone, you can use the same app/phone to cancel your ride and complain.