Usually, the microcontroller pin that is used for switching the relay, is not shorted with the COM pin of the relay. If you take single-channel relay boards into consideration, you will see that the microcontroller pin is usually connected to the base of a transistor via a resistor as you can see in this diagram:
https://www.researchgate.net/figure/Rel ... _341570650There must a something like this in your board too.
So, the continuity test at the COM pin is not gonna help. You have to figure out which pin of the ESP is connected to a transistor base via a resistor.
From the photo of your board, it looks like there is an opto coupler. In that case your have to figure out which ESP pin is connected to the optocoupler's input.