The STEC 30 (at least as installed in your plane and mine [#1116, so roughly the same age as yours]) does not come with GPSS, although you can add it aftermarket for a fairly reasonable price.
Without GPSS, the Stec 30 will not track major course changes in the GPS track - in other words, it might happen to track a 5 degree heading change okay (if the OBS is adjusted accordingly), but you can’t expect it to track a 30-45 degree or more change.
With the stock STEC 30, you’re supposed to hand-fly on course, and then once established, you can activate NAV tracking. (You can’t even have the A/P intercept a course like the System 55/55X.)
GPSS is a worthwhile investment and will make the A/P work more similarly to the Garmin simulator (but there are still important differences that you’ll want to read up on.)