scatter + histogram example using mpl `insert_axes` does not work

Start by running the provided scatter-and-histogram example, comparing the subplot_mosaic and inset_axes sections and their rendered output. Trace the inset_axes layout and rendering path used by the example. Done means the marginal axes render separately in the expected positions without stacking over the main plot.

https://matplotlib.org/stable/gallery/lines_bars_and_markers/scatter_hist.html

"""
============================
Scatter plot with histograms
============================

Add histograms to the x-axes and y-axes margins of a scatter plot.

This layout features a central scatter plot illustrating the relationship
between x and y, a histogram at the top displaying the distribution of x, and a
histogram on the right showing the distribution of y.

For a nice alignment of the main Axes with the marginals, two options are shown
below:

.. contents::
   :local:

While `.Axes.inset_axes` may be a bit more complex, it allows correct handling
of main Axes with a fixed aspect ratio.

Let us first define a function that takes x and y data as input, as well as
three Axes, the main Axes for the scatter, and two marginal Axes. It will then
create the scatter and histograms inside the provided Axes.
"""

import xy.pyplot as plt
import numpy as np

# Fixing random state for reproducibility
np.random.seed(19680801)

# some random data
x = np.random.randn(1000)
y = np.random.randn(1000)


def scatter_hist(x, y, ax, ax_histx, ax_histy):
    # no labels
    ax_histx.tick_params(axis="x", labelbottom=False)
    ax_histy.tick_params(axis="y", labelleft=False)

    # the scatter plot:
    ax.scatter(x, y)

    # now determine nice limits by hand:
    binwidth = 0.25
    xymax = max(np.max(np.abs(x)), np.max(np.abs(y)))
    lim = (int(xymax/binwidth) + 1) * binwidth

    bins = np.arange(-lim, lim + binwidth, binwidth)
    ax_histx.hist(x, bins=bins)
    ax_histy.hist(y, bins=bins, orientation='horizontal')


# %%
# Defining the Axes positions using subplot_mosaic
# ------------------------------------------------
#
# We use the `~.pyplot.subplot_mosaic` function to define the positions and
# names of the three axes; the empty axes is specified by ``'.'``.  We manually
# specify the size of the figure, and can make the different axes have
# different sizes by specifying the *width_ratios* and *height_ratios*
# arguments. The *layout* argument is set to ``'constrained'`` to optimize the
# spacing between the axes.

fig, axs = plt.subplot_mosaic([['histx', '.'],
                               ['scatter', 'histy']],
                              figsize=(6, 6),
                              width_ratios=(4, 1), height_ratios=(1, 4),
                              layout='constrained')
scatter_hist(x, y, axs['scatter'], axs['histx'], axs['histy'])


# %%
#
# Defining the Axes positions using inset_axes
# --------------------------------------------
#
# `~.Axes.inset_axes` can be used to position marginals *outside* the main
# Axes.  The advantage of doing so is that the aspect ratio of the main Axes
# can be fixed, and the marginals will always be drawn relative to the position
# of the Axes.

# Create a Figure, which doesn't have to be square.
fig = plt.figure(layout='constrained')
# Create the main Axes.
ax = fig.add_subplot()
# The main Axes' aspect can be fixed.
ax.set_aspect('equal')
# Create marginal Axes, which have 25% of the size of the main Axes.  Note that
# the inset Axes are positioned *outside* (on the right and the top) of the
# main Axes, by specifying axes coordinates greater than 1.  Axes coordinates
# less than 0 would likewise specify positions on the left and the bottom of
# the main Axes.
ax_histx = ax.inset_axes([0, 1.05, 1, 0.25], sharex=ax)
ax_histy = ax.inset_axes([1.05, 0, 0.25, 1], sharey=ax)
# Draw the scatter plot and marginals.
scatter_hist(x, y, ax, ax_histx, ax_histy)

plt.show()


# %%
#
# While we recommend using one of the two methods described above, there are
# number of other ways to achieve a similar layout:
#
# - The Axes can be positioned manually in relative coordinates using
#   `~matplotlib.figure.Figure.add_axes`.
# - A gridspec can be used to create the layout
#   (`~matplotlib.figure.Figure.add_gridspec`) and adding only the three desired
#   axes (`~matplotlib.figure.Figure.add_subplot`).
# - Four subplots can be created  using `~.pyplot.subplots`,  and the unused
#   axes in the upper right can be removed manually.
# - The ``axes_grid1`` toolkit can be used, as shown in
#   :doc:`/gallery/axes_grid1/scatter_hist_locatable_axes`.
#
# .. admonition:: References
#
#    The use of the following functions, methods, classes and modules is shown
#    in this example:
#
#    - `matplotlib.figure.Figure.subplot_mosaic`
#    - `matplotlib.pyplot.subplot_mosaic`
#    - `matplotlib.figure.Figure.add_subplot`
#    - `matplotlib.axes.Axes.inset_axes`
#    - `matplotlib.axes.Axes.scatter`
#    - `matplotlib.axes.Axes.hist`
#
# .. tags::
#
#    component: axes
#    plot-type: scatter
#    plot-type: histogram
#    level: intermediate

The subplot_mosaic method renders as expected, but the insert_axes method seems to stack everything on top of each other and doesn't render correctly.

This is ignoring the usability issue on subplot_mosaic where the pan/zoom between the 3 plots are not synced -- i think that's a separate issue.