ST3 is an input jack that you could connect to the headphone output on your computer.
The larger 1/4 inch jack is the mixers headphone output jack.
ST3 may need to be patched/assigned to the ST3 fader, you can do that from any channels assignment patch menu from the pre amp menu screen. You want ST3 set to local.
You could always connect the computer to the either ST1 or ST2 on the back of the mixer.
A digital mixer of any kind that has had lots of people using it may have some interesting settings and routing configurations set up!!!!