Multivar colorbar - #32607

This PR has a long history. It is part of Bivariate and Multivariate Colormapping and contains changes that were previously part of #31214 which is being separated into multiple parts with the use of AI. This is part 3 of 4 and Depends on #32605 and #32606. Only the last commit ("Add multivariate colorbars") is new in this PR.

PR summary

• Adds Figure.colorbar_multivar / SubFigure.colorbar_multivar and pyplot.colorbar_multivar.
  MultivarColorbar (in matplotlib.colorbar_multivariate) is a Sequence of ordinary Colorbar objects, one per variable, as jklymak suggested in Multivar colorbar #31214.
• make_multivar_axes takes the space for the whole block through the existing colorbar.make_axes (as for a single colorbar), then splits it into one Axes per variable.
• n_major arranges the colorbars in several rows/columns; major_pad / minor_pad set the spacing.
  Colorbars can also be drawn into user-supplied Axes with caxes=.
• Figure.colorbar raises a clear error for multivariate colormaps, pointing to colorbar_multivar.
• Release note with a plot in doc/release/next_whats_new/colorbar_multivar.rst.

NOTE:

• Constrained layout is not supported in this PR: it raises a NotImplementedError unless caxes is given. Support follows in part 4, kept separate so the layout-engine changes can be reviewed on their own.

There is no example in the docs yet, that will come in a separate PR.

Here is an example:

im_A = np.arange(200)[np.newaxis, :]*np.ones((200, 200))
im_B = np.arange(200)[:, np.newaxis]*np.ones((200, 200))
im_C = 0.9*im_A + 0.9*im_B

im_A = np.sin(im_A**0.5)**2
im_B = np.sin(im_B**0.5)**2
im_C = np.sin(im_C**0.5)**2

fig, axes = plt.subplots(2, 2, figsize = (10, 6), dpi = 100)
axes = axes.ravel()
locs = ['right', 'left',  'top', 'bottom']

im = (im_A, im_B, im_C)
for i, loc in enumerate(locs):
    cim = axes[i].pcolormesh(im, cmap='3VarAddA', vmax=(1, 1, 1))
    cb = fig.colorbar_multivar(cim, location=loc, n_major=2)
    cb[0].set_label('A')
    cb[1].set_label('B')
    cb[2].set_label('C')

fig.show()

AI Disclosure

The split of #31214 into smaller PRs, and the changes requested in review there, were
made with the assistance of an AI coding assistant (Claude). All changes were reviewed
and tested by me.

PR quality check

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