Why does the voltage drop when I connect an 8 ohms 1 watt speaker, specifically the source to the circuit is GPIO pin output voltage?
You need to do something like this:



simulate this circuit &ndash; Schematic created using CircuitLab
That delivers power to the speaker as needed, but allows you to turn on the BT66 (which seems to be an FM radio receiver) with the signal from your GPIO pin.
As has already been noted, IO pins from microprocessors aren't intended to provide power.  They are control or data signals, and cannot provide high current.

The above sketch assumes that the BT66 is powered from something appropriate.  You didn't show the power connections for it in your sketches, and I didn't make an effort to find a datasheet or other description of it.