I would have to agree with Richard in part that the whole picture would help in responding to help in a more educated manner if we saw the whole picture and not just bits.
I will do what I can with what I see;
I see a cantilivered framing support of a breakfast Nook that is about 4’-6’ out from the main building.
Not seeing the whole picture, there is no way of knowing if the framing is cantilevered or an add on.
It appears that the long slender post are picking up the weight of the Nook which wouldbe an idicative that the framing for this nook, might not be cantilivered but an add on.
The post seem to be of a six x eight inch in size based on the built-up beam that consist of four members= 6"
The post overhangs the beam and toenails for attachment.
Thus, 7-1/2" post support.
It is possible that the post is off centered with the beam.
The post and beam attachment should have had something similar to
The chchecks in the wood post would be idicative of high moisture content of 30% at the time of installation and if the check is on only one side might not be a concern.
A full check to both sides might provide failure in the future and is well to note it as you see it.
The post are anchored at the base to provide lateral displacement in that connection.
The concrete sonotube bases although not perfectly plumb appear to be adequate.
The overall picture from what I see, this Nook is adequately supported.
The whole picture of the surroundings might show a different story, and that is why a panorama of the detailed pictures is important to make an assessment.
So the big question in my mind on something like this would be, are those post carrying a load or are they an aesthetic feature?
The latter would be of no concern.
I think this was a good pick up on your part and well noted to cover all bases.
It is better to note what you see than trying to figure out what the structural problem may be.
Recommend and Architect to review and question whether or not drawings from a designer are available or were provided for this build.
Hope this helps.