With the commit before the AnyIO PR on the main branch (830829f) and using ipython 8.23.0 and matplotlib 3.8.4, the displaying of Matplotlib plots in separate windows (e.g. with qt backend) using jupyter works fine. With the AnyIO commit (772dfb8) onwards the plot windows are no longer displayed.
Code to reproduce (I've been using jupyter qtconsole but jupyter lab, etc, all show the same):
%matplotlib qt
import matplotlib.pyplot as plt
fig, ax = plt.subplots()
ax.plot([1, 3, 2])
In ipython the same example works fine.