I found a solution for Studio One Version 3:
In Options Advanced Midi I choose Use legacy Midi insted of direct music.
In External Devices I made a Keyboard device and an Instrument device, here I choose Send Midi clock and Send Midi Clock start.
The Timing is now perfect.
But: I must choose a the smallest (64 samples) or a small buffer size in my Steinberg UR22 soundcard. If I uncheck Use legacy Midi insted of direct music the timing goes bad.
I misunderstood the sync knob settings of Beatstep Pro, INT and USB sends MIDI and clock out over USB and the MIDI out socket, MIDI means an external device is connect over MIDI in socket and clock means that a DIN SYNC device is connected over clock in socket.