Which supply to use

SIGNAL is VCC

Pick your board, then try both supplies. With the switch on, SIGNAL is joined to VCC through a closed contact, so it carries whatever VCC carries. The block has no regulator and no level shifting. Choosing VCC is choosing the voltage your input pin will see.

3V3 beside a 3.3 V board

An ESP32, an ESP32-S3 and a Pico all run their pins at 3.3 V, and none of them is rated for much above it: each chip's datasheet allows only a few tenths of a volt over its own supply. Feed the block from 5V and every time the switch is on, 5 V sits on the pin.

It will read HIGH and it will seem to work, which is what makes it expensive. The damage builds up inside the pin and does not announce itself. The fix costs nothing: wire VCC to the board's 3V3 pin. The input reads 3.3 V as HIGH with room to spare, and the LED still lights, a little dimmer.

5V on an Uno

An Uno runs its pins at 5 V, so 5V is right. 3V3 also works, narrowly: the Uno's chip, the ATmega328P, guarantees to read anything above 0.6 × 5 V = 3.0 V as HIGH, and 3.3 V clears that by 0.3 V. There is no reason to take the narrow option.

Not wired at all

The one wiring that never works is no VCC. The switch closes onto a pin that carries nothing, the pull-down holds SIGNAL at 0 V, and it reads LOW in both positions. The LED stays dark too, because it is fed through the switch. If the block seems completely dead, VCC is the first wire to look at.

The TK01 XL LED has no VCC pin, and it is easy to carry that habit over. This block needs all three: GND, VCC and SIGNAL.