Yeah, I find it hard to believe this device could be sold for $4.99 at a profit, if you count up BOM, assembly and logistics related to sending it. But given that some posters mention Amazon actually gives you $4.99 back for the first purchase, they must not be caring.

Anyway, here's a teardown I found:

https://mpetroff.net/2015/05/amazon-dash-button-teardown/

Now a surprising thing that I didn't know before - this thing has a microphone on board. Yes. Yet another Internet-connected microphone. Apparently used only to configure the button via ultrasound, but I wonder how hard would be to repurpose it...