Just as a data point: Current state-of-the-art methods for Lanczos-type methods on state vectors are around 40 spins/qubits incorporating many symmetries and additional shortcuts one does not have in a generic "quantum computer simulator". Without those symmetries/shortcuts, the limit is likely closer to 30 qubits (i.e. approx. 16-64 GB per state vector), as it’s not only necessary to store these beasts but also do operations on them.

If you don’t insist on a single dense state vector but a sparser tensor network-based formulation, you can go to much larger systems (hundreds or thousands of spins) but will be limited by the amount of entanglement you can represent in your system.