Simple momentary push buttons can be made dirt cheap in quantity. Push-push switches, definitely not. The cost ratio between a momentary switch plus a bit of electronicselectronics*, vs. a mechanical push-push switch, is huge. As a bonus, a momentary plus electronics is cheaper to make reliable.
So on a cheap consumer product, the on/off switch is almost certainly implemented by a momentary switch plus some circuitry. For any given product, you'll have to do a visual inspection, plus maybe some poking around with a multimeter.
* And if the product has a microcontroller in it, that "bit of electronics" can easily be the microcontroller itself.