I very much doubt that such studies exist, or that they even would be able to provide an answer to the question how the Trump presidency influences the Overton window.
There are two reasons for this. First, the actual Overton window is difficult to quantify. You can ask people what they would think about certain statements, but especially when topics diverge into the "radical" or even "unthinkable" region, people do not tend to be honest because they do not dare to confess (maybe not even in front of themselves) that they are thinking unthinkable or outrageous thoughts. You also can check the coverage of certain topics by the media, but it is difficult to assert if an idea is not discussed because of being perceived as too radical or because it simply is not present (or seems illogical) in the mind of the writer. Note that by definition the Overton window is about what people do not say, and that is very problematic, if not impossible, to access.
But even if we assume that there is some sort of reliable metric to measure the Overton window, studies will only be able to see a correlation between the Overton window and the Trump presidency, but not a causation. Assume that we find a shift of the window to a certain direction during the Trump presidency, does that mean that Trump is responsible? It might be the other way round: The shift of the window might have made Trump possible in the first place, and it continues during his presidency. It also might be that there is a third reason that creates the shift as well as made Trump president. Or it may be a simple coincidence, which given the very small statistical data is also very much possible.
Note how difficult it is to answer similar questions with easy to access parameters like "unemployment rates". Did the Obama presidency reduce the unemployment rate? Or were other reasons prevalent and Obama just profited from those?
Thus even if there was a measurable correlation, it would be a far stretch to conclude that "Trump shifted the Overton window".