Sorry, a bit confused.
If the wind instrument is working on its own, then the wind speed you are reading is pure apparent speed, nothing to do with true. The only time the wind in this condition can be considered true is if the boat is guaranteed to be stationary i.e. anchored. The true and apparent become one. As soon as the boat begins to move in any direction, the wind is apparent and not true.
Only if a boat speed indicator is working in the same NMEA system with the wind speed and direction can the readings be vectored to produce true wind speed. And the calculation of true wind speed done by the wind instrument and the boat speed indicator working together has no reference to course or heading or any other such dimension.
How do I know this? I had a protracted argument years ago with Sailing Dog who successfully proved that I was wrong and the correct answer is as outlined above.
I completely agree, at least with the part where you say "a bit confused". Me too.
Here is what I was trying to say, when it comes to calculating true wind direction relative to the course of the boat, there needs to be three pieces of information. The first is the apparent windspeed from the wind instrument, the second is the apparent wind angle to the center line of the boat, and the third is the speed of the boat. Crunching the numbers produces a true wind angle relative to the centerline if the boat.
The source of the speed data typically comes from one of two sources, either the GPS SOG, or from the knotmeter speed through the water. If the data comes from the GPS SOG, then current is automatically factored in and so that would calculate the true wind that you might measure if you were anchored. If the data came from the knotmeter, it has no way of measuring current and so the calculated true wind would approximate the wind that you would measure if you were drifting with the current.
And if you wanted to know the compass course of that wind, the instruments would need data from an electronic compass, in which case, it would then do the arithmentic to add or subtract the angle of the true wind to the boat's course, COG being irrelevant to that calculation.