AnyIO commit breaks Matplotlib display in separate windows

With the commit before the AnyIO PR on the `main` branch (830829fd) 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 (772dfb8a) 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):
```python
%matplotlib qt
import matplotlib.pyplot as plt
fig, ax = plt.subplots()
ax.plot([1, 3, 2])
```

In `ipython` the same example works fine.