Automated clip path generation should sometimes use intersection

Nobody has claimed this yet.

In #23199 a change was introduced that does not overwrite the clip path if already set. There is one corner case that generates a new problem. Figure.add_artist(..., clip=True) used to clip based on "figure", but there is a (possibly artificial) case where it would be better to add an intersection of the figure and the set clip path. I guess that in general, it can be useful to have polygon intersection support, although it is a non-trivial case where we may want to rely on some external library. There are probably several issues that benefit from this, but at least #23454.

However, for this specific case, it may be a bit easier since we know that at least the figure is convex (a box) so it may be possible to solve it separately.

---

I think this is an example that shows that it is better to use the intersection:
```
import matplotlib as mpl
from matplotlib import pyplot as plt

fig, ax = plt.subplots()
poly3 = mpl.patches.Polygon([[-0.5, 0], [-0.5, 0.5], [0.5, 0.5], [0.5, 0]],
facecolor="g", edgecolor="y", linewidth=2, alpha=0.3)

fig.add_artist(poly3, clip=True)

line = mpl.lines.Line2D((-1, 1), (0.25, 0.25), color='r', clip_on=True, clip_path=poly3)
ax.add_artist(line)
# or
# fig.add_artist(line, clip=True)
```

With this PR one gets

while current master gives


or


_Originally posted by @oscargus in https://github.com/matplotlib/matplotlib/pull/23199#discussion_r1125638275_

Start with the example in the issue and inspect the clip handling changed by #23199, especially the path used by Figure.add_artist(..., clip=True). Compare the existing figure clip path with an explicitly set clip path; done means the rendered result is clipped to their intersection without changing unaffected cases, with regression coverage for this example.

Written by the indexing model from the issue text.