Bug report

Bug summary
The webAgg backend reports middle click events as right click events. This is caused by these lines:

I don't think I entirely understand the issue described by that comment but I'd argue that it is better to allow users to make the choice to listen for middle clicks rather than to report middle click as right click. Also there does not seem be anything in MouseEvent docstring about this: https://matplotlib.org/3.3.0/api/backend_bases_api.html#matplotlib.backend_bases.MouseEvent

I ran into this when using the ipympl backend (xref matplotlib/ipympl#254)
Code for reproduction

In the notebook:

import ipywidgets as widget
import matplotlib.pyplot as plt
%matplotlib widget

out = widgets.Output()
@out.capture()
def callback(event):
    print(event.button)
    
plt.ioff(); fig,ax = plt.subplots(); plt.ion()
fig.canvas.mpl_connect('button_press_event', callback)
fs = 15
ax.text(0.1,0.1,'left click here', fontsize=fs)
ax.text(0.5,0.5,'middle click here', fontsize=fs)
ax.text(0.7,0.8,'right click here', fontsize=fs)
widgets.HBox([out,fig.canvas])

Actual outcome

Expected outcome
in ipython it gives this

Matplotlib version

• Operating system: Ubuntu 20.04
• Matplotlib version: 3.30
• Matplotlib backend (print(matplotlib.get_backend())): 'module://ipympl.backend_nbagg'
• Python version: 3.8.5
• Jupyter version (if applicable): jupyterlab 2.2.0