Optimal segment length for coherence estimation
There is good news and bad news. You are actually showing magnitude squared coherence(MSC). There is a very complete treatment of MSC, including closed form equations for the sample MSC as a function of independent samples.  There is also a discussion on overlap in:

    G. C. Carter, “Coherence and time delay estimation,”
 Proceedings of the IEEE, vol. 75, no. 2, pp. 236–255, 1987


The bad news is in the plot, which is the sample pdf for MSC where the true MSC is .3, in a single bin where the legend denotes the number of independent terms. If you want 256 frequency bins,  you really need around $256^2$ data points.



You might want to look up the paper and note any recent citations where there is some scheme to reduce the amount of data you need,  but 256 points is not anywhere near enough.