If it were my home I would definitely use a 1/2" anchor in the center of the post.
There is no need to jack it up, since when you tighten the nut and washer on the anchor it will have a lot of leverage to lift it if it is needed.
I would also use a tie plate to fasten the beam to the top of the post. Or pair of them.
For ten dollars, don't fret over it and get it done.
It may be drying... but then when boards dry they get shorter and reduce the load so the post should have a tendency to loosen up, not get more pressure on it if the warpage is due to drying.
Also, there is an air space between a couple of the 2x4 indicating they are not properly laminated together. The anchor will help that. And on that note, again, laminating three boards together tends to minimize warpage as the stresses in each board is different and can have a tendency to counteract and negate warpage in the other boards.
Sooooo, the warpage is likely from settling.
Also, again, stuff tends to settle more, not less, as time goes on, so any defect you are seeing now will only get worse, never better.
I would not wait until it starts to show signs of damaging finished work in other areas of the house.