I find the vendor datasheet helpful and void of some misleading information.
The HC-06 module is pretty versatile, but most devices on the market are build only with RS232 / serial access.
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The HC-06 has a reset / rst I/O pin but it is doubtful that is is the same as "key" or "Wake-up" pins on the RS232 BT device interface pins. .
I have not found single "how to use BT " explaining functions of "Key" or "Wake-up".
One article recommended to keep the "key" at level (?) , don't remember if HIGH or LOW, during BT power up than change it to opposite to "initialize ".
From that it seems that both ( KEY or Wake-up) can be used to initialize the serial connection with BT, the question remains does that means Arduino , as it case may be , to BT serial / modem connection or Arduino to other BT device
It won't cause no harm to try there signals ( Key or Wake-up) , maybe they can function as kind of reset.