Replacing broken road fork with same model but shorter steerer tube. What can I expect for handling issues?
Steering will not really be directly affected at all, because you are not changing the steerer tube angle, fork length or rake, or the stem length.

What will be affected is your riding position. Dropping your bar 30mm is a big adjustment. (BTW, standard steerer tube spacers are 5mm, so you may want to check that you can actually drop your stem 30mm.)

You really need to ask yourself if you can tolerate such a big drop in your handlebar position, or even if it would be desirable.

You could possibly replace the stem with one with a greater rise angle to bring the handlebar back up.