Fix app icon bug on Windows when running IPython - #32360

PR summary

When running IPython on Windows and using one of the Tk backends, the app icon for a new matplotlib window can incorrectly be the default Tk icon instead of the matplotlib icon. Apparently the IPython event loop suppresses the Tk event loop in such a manner that the setting of the app icon may not go through if Tk has not been used for a while in the IPython session.

To see the bug, run the following on Windows in an interactive IPython session:

import matplotlib
matplotlib.use('tkagg')  # TkCairo is also bugged
import matplotlib.pyplot as plt

plt.figure(); plt.show()
# note the correct matplotlib icon

# close the window, and then wait ~10 seconds

plt.figure(); plt.show()
# note the incorrect icon

# close the window and do not wait before continuing

plt.figure(); plt.show()
# note the correct icon

This PR explicitly calls .update() right after setting the icon to ensure that the icon change is actually processed. (calling update() is discouraged, xref #17789)

This PR moves the icon-setting code to right after the new window is shown for the first time, and the bug stops happening.

AI Disclosure

No AI was used

PR quality check

• Use an expressive title, e.g. "Fix title font property precedence"
• [N/A] New and changed code is tested
• [N/A] Plotting related features are demonstrated in an example
• [N/A] New features and API changes have release notes
• [N/A] Documentation complies with general and docstring guidelines