There is actually a subforum dedicated to the Score Editor, perhaps a mod will move this.
There are two ways you can setup the Score Editor to deal with multiple staves. This is done on the the Score Setting’s Polyphony Tab.
The simplest but least flexible is to set it to Split. By default this is set to Middle C (C3) but you can change it. With a Split set on C3 then all notes C3 and higher will end up on the treble stave; and all notes B2 or lower end up on the bass stave. The problem is the right hand can’t go below C3 and the left can’t go above B2.
The more flexible and complicated setting is to Polyphony. This determines which stave a note belongs to based on MIDI Channel number. Again you can change these, but the default is Channels 1 & 2 will be on the treble stave and Channels 3 & 4 in the bass which works well for SATB. This method will use ledger lines to go above and below C3 on both staves.