Underrated microswitch in consumer product odd?
Summary: Although I can't analyse the other sensors you mentioned using the photos, switch SW1 is not carrying mains voltage.

Doesn't look like there's any voltage conversion circuitry

I bet there is. At the very least, the start/stop button won't usually have mains voltage on it, since the power for motors etc. doesn't pass through that, as the power to the motors continues even after the button is released. So my hypothesis is that the buttons are not carrying mains voltage and so their rating is sufficient.
A quick look at the new photos of the PCB confirms my hypothesis. They show a capacitive dropper type of power supply (that's the reason for the large yellow capacitor), what looks like a power diode for rectification (we can see N4 in its part number e.g. perhaps 1N4007 or similar), a possible zener diode for regulation (we can see 39 in its part number - perhaps a 3.9 V zener?), and an electrolytic capacitor for smoothing.
Note: This type of power supply means that the DC side of the device is not isolated from mains, and therefore should be treated as dangerous when energised.
If you are going to connect signals from inside this unit to other devices (you mentioned modifying it for automation), you must investigate techniques like opto-isolators.

The switch in discussion in SW1 at the top centre of the board

That is on the DC side of the power supply, and isn't switching mains voltages.
The circuitry also includes a PIC12F MCU controlling device TR1 (a triac?) via a bipolar transistor Q2 (we can just see markings for E and C) to switch the AC motor voltage (actually switching the ACN incoming mains wire, so probably the neutral) to terminal M+.
After more review of the photos, SW1 is switching a logic-level signal to pin 3 on the PIC12F. That again confirms that it is switching a low-level signal and not mains voltage. Therefore its 3 A/125 VAC rating is not an issue.