How is mixing time influenced when using a sourdough starter?

I am new to producing and using a sourdough starter at home. While mixing a dough that incorporates a starter using a stand mixer with a dough hook attachment, I have observed the resulting dough looking much less smooth than a standard yeast dough. My question is if and how using a sourdough starter has an impact on mixing (kneading) speed and time.

The image above shows the surface of the dough is not smooth. It is quite elastic, though.

For context, I converted a standard yeast recipe (Italian bread) to allow incorporating the starter. The primary purpose of this is for additional flavor. This recipe is by weight and I used the ratio of the starter's flour and water to formulate the converted recipe. Base recipe mixing time calls for 8 - 10 minutes at second speed.

I have tried two methods of mixing when incorporating a starter (both are variants of the straight dough method). First I tried adding all ingredients at once, including the starter, and mixing. The second method I tried was adding all ingredients except the starter, mixing until a rough dough was formed, then adding the starter and finishing the mixing. Both methods produced a similar dough with a bumpy exterior. Compared to the base recipe, the dough is much more elastic and more sticky (though I'm not sure if it is more "wet" or just the norm when a preferment is added).

I should mention the resulting loaf had good flavor and form but the texture was more dense than I desire. There are still a number of factors I will work on tweaking and improving but I'd like to rule out over (or under) kneading as a factor. I have significant experience with yeast breads but am lacking accurate knowledge of how a sourdough starter impacts various aspects (mixing, fermentation, proofing) of bread making. I did some Googling and also searched Cooking SE but am not finding an answer to this specific question.