How do I know when my 100$ search ads promo credit is exhausted?
I don't think there's a specific way to know.  I have the promo $100, too, and I was looking into this.

The only way I found out was to check on the available balance every few weeks.  Even doing that, you have to accept that you might go over the promo amount.  Of course, this is exactly what Apple is hoping will happen (in my personal opinion; I don't have any proof for that).