Smoke or steam????

You mention "connected to". Does this mean the stove exhaust is in contact with the masonry, not contained inside a 3-4" ss pipe? If it is in contact with the masonry, and in your area, have had some recent rains, it is possible to be moisture. But "steam" will only stay as visible vapor for a very short time and distance from your chimney. Smoke is a particulate matter that will stay visible for extended distance and periods of time.

Is it still smoking or steaming after a few more hours or running? It is possible that the first run of the season in your climate may dry thing out regardless of cover over the summer and fall. Foggy days and high humidity for a while can cause moisture to collect pretty much anywhere. A little heat and things dry out, sometimes causing a bit of steam. Kinda like putting a sweat shirt in the dryer after going for a walk when the rain came in earlier than forecasted, steam comes out the dryer exhaust. Hopefully that is all it is, and not smoke from a stove issue.

One must remember that the products of combustion are water and carbon dioxide. Burning pellets that are usually around 7-8 % moisture.
Depending on the environment the exhaust is venting into, RH, temperature, barometric pressure etc all come into play in noticing the water vapor of smoke. Just like one does not always see car exhaust.

I usually see white smoke from my chimney. Not a big deal

Interesting. Other than start up and shut down, there is no visible exhaust from my pellet stoves at any temps so far. Had 16 degrees F last week. Nothing out the exhaust beyond about 20 seconds at start up and again at shut down. But then, my exhaust chimneys are only 2' horizontal, then 6' vertical.