The spokes are an easy fix, as you described but my experience of breaking spokes is that more break later down the line. It’s usually due to crap quality spokes more than anything. Either replace the spokes or the whole wheel. Decent tough spokes are not expensive but can take a while if you haven’t done the job before.
My suspicion is the spokes are crap. Not an old wheel by any stretch and it wasn't under that much stress when I heard the dreaded ping. And no, I haven't done this before, so the idea of replacing the lot with decent tough spokes isn't appealing.
The spokes are an easy fix, as you described but my experience of breaking spokes is that more break later down the line. It’s usually due to crap quality spokes more than anything. Either replace the spokes or the whole wheel. Decent tough spokes are not expensive but can take a while if you haven’t done the job before.