Latching push button with electronic reset
When you look at the unit price of the switch that you found it becomes pretty obvious for most projects that another approach is more appropriate. A momentary tact switch can be made to operate in a push push toggle mode. Some low cost tact switches even have integrated LEDs to light the knob or button. If the lowest cost approach is used an SMT LED is located just adjacent to the tact switch on the board.

It is possible to design circuitry that implements the current state holding for the toggle status however these days when virtually every gadget has a microprocessor embedded into it it makes a lot of sense for the MCU to monitor the tact switch presses, de-bounce them and the track the toggle state in a memory location. The MCU can then also control the state LED via another output pin. A huge advantage of this approach is that the toggle state can be kept in a serial EEPROM byte so that when there is a power loss / restore the toggle state can be set back to what it was last set to.