Interactive plots do not work (no PyOS_InputHook)

I noticed that when using PySide as a backend for Matplotlib, plots do not work in the interactive interpreter (they do not open). This is in contrast to PyQt, where this works. I think the reason is that PySide does not implement the
PyOS_InputHook API, which allows the event loop to run in the background.

Here's a minimal example to reproduce the issue (this assumes that both PySide6 and matplotlib packages are installed; it is important that PyQt6 is not installed simultaneously):

• Start the interactive interpreter: python
• Run the following commands (line by line):

import matplotlib
import matplotlib.pyplot as plt

matplotlib.use("QtAgg")  # will use PySide6
plt.ion()  # turn on interactive mode
plt.plot(1)  # should open a figure, but this does not work

Note that in this example, if you install PyQt6 instead of PySide6, everything works (the figure opens as expected).

Note also that this example does work in IPython, even with PySide, because IPython provides its own input hook.

Some additional discussion can be found here: https://github.com/matplotlib/matplotlib/issues/15359#issuecomment-1380734369