• Ok,

    I meanwhile managed to pair the HC-05 with my Mac.

    It seems that the intensity of the chip's BT signal is so low (especially compared to all other BT devices I'm currently using) that my Mac simply did not receive it properly. Bringing it closer to my computer solved the "problem".

    Keep that in mind when you try yourself!

    Additional note: once paired, the special "trick" for macOS mentioned in the original instructions does not seem to be necessary any longer: Chrome now properly recognizes Bluetooth serial ports as well.