MDBT42Q no polarity protection?

Argh, sorry you've had problems. Maybe you could try powering it via 3.3v and see if it still works?
While the board itself doesn't have reverse polarity protection, I believe it's the voltage regulator that most likely gets blown up, not the chip.

Usually it's pretty robust. I just connected one backwards to a LiPo here to see what would happen and the voltage regulator started smoking, but the board still worked when I turned the voltage back around.

I remember I made wrong connection with pico, but there is rectifying diode

There's a rectifying diode on USB since you have the voltage, but on the battery pin it has to use a FET (because you can't afford to have the voltage drop). There wasn't enough board space on the MDBT42 to fit that in unfortunately.