@Marc, can you share a pic of the button?
Does your screw driver have an insulating handle?
It sound to me as if the button part that you touch has some conductivity and connects 'you' with the pin. Depending on the 'electro smog' you are in, this make the pin to sense edges and triggers by setWatch(). To verify this in an experiment: remove the button, stand free, take a shot piece of blank wire and touch B10...
Furthermore, I was reading your post #4 where you describe vaguely what else is going on. Do you know the power drawn by these number of outputs? I'm going on a goose chase here, but it could well be that in addition to the button issue, there is a power issue going on. Even though the chip can source/drain 20mA with guaranteed levels per pin, there is a total of power that can be sourced and that is max 120mA - p59 of STM32F401xD datasheet.
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