Am I Covered by the Visa Amnesty Until the End of July?

You will indeed covered by the amnesty AFTER your current extension stamp good until the 18th of May expires. The amnesty will cover you until no longer than July 31st.

Don't think of it as a "free 3 month pass" to thailand though, you need to watch when the borders open and see what announcements are made regarding amnesty holders once they do (how fast you need to exit thailand).

BUT

At this time you don't need to go to the immigration office or do anything other than pay attention to the news :)