Hi ,Jcf
Next please masure voltages according to ground(gnd) at pins rx, tx, vcc(5V) of the bluetooth module directly on it and let me know the result.

Does bluetooth module soldered directly to the red main board or is there black connector where the module is inserted?

When you connected it to wires at first time - was there a connection via bluetooth?

Hi Pin, I apologize for my long delay in answering, it's been a while since I've had any time to tinker !
I have the following voltages on the Bluetooth module pins :
RX : 5V
TX : 1,26
VCC : 5V
Yes, the Bluetooth module is soldered, and yes, it was working at the beginning and I did my first recordings thru it, and there is still an HC06 Bluetooth registered in my computer connections.

Hi JCF,
Sorry for delay with answer.

I think the bluetooth module is dead :(
Typically they dying if something was shorted or it could be killed by static.
Now you need to replace the module.
Cut it with a pliers from the board, next you will need to remove carefully remaining pins with a soldering iron and install 2.54mm pitch socket ( or solder new module directly to the board)
Вложение 2616
I recommend you to install a socket, becuse you can buy fake module or it culd be damaged again, so the socket makes replacing more easy.
There is a lot fake HC-06 modules on aliexpress and other shops and I not recomend to use it. It will be better to by JDY-33 or JDY-31 module.
Or if you can by genuine HC-06 - you can buy and use it.

Please write about result after replacing the module.