Replace the SimilaritySurface hierarchy with categories

[saraedum]

Fixes #132 and hopefully gets rid of all of the boilerplate that is currently necessary to expose functionality in both surface hierarchies.

Checklist

• [x] Added an entry in doc/news/.
• [x] Added a test for this change.
• [x] Added new .py files to the documentation in doc/geometry or doc/graphical.

Dependencies

• [x] #219
• [x] #221
• [x] #223
• [x] https://github.com/flatsurf/exact-real/issues/172
• [x] https://github.com/flatsurf/exact-real/issues/173

TODO

• [x] We cannot compute the stratum of some half-translation surfaces. See https://sagemath.zulipchat.com/#narrow/stream/271193-polygon/topic/category/near/355786162.2E01. This now shows as an error when printing these surfaces. (postponed as #227)
• [x] __eq__ should be a very strict notion of equality always (same type & indistinguishable); make sure this is always the case and documented
• [x] labels() does not work for non-connected surfaces; this is not a new problem. There is only a single base label so how should we iterate non-connected surfaces?
• [x] Make sure that all the example constructions still work (except for the ones defining infinite surfaces.)
• [x] Make sure that there are no new #TODO markers in the code anymore.
• [x] Speed up doctests (we are now doctesting much more through categories, and tests take about 55 seconds on my machine which is annoying.)
• [x] Document what's at the bottom of surface.py.

Fix Speed Regressions

Generically, some tests deteriorated:

• [x] similarity_surface.py + rational_similarity_surface.py 3s → 11.2s → 5.6s → 3s
• [x] delaunay.py 2.16s → 15.03s → 4s
• [x] fundamental_group.py 0.29s → 0.97s → 0.19s
• [x] mappings.py 0.37s → 0.82s → 0.4s

There are specific problems with performance:

• [x] is_rational_surface() (which is new) is very slow. (but it's not called automatically anymore.)
• [x] printing of surfaces is sometimes very slow

[saraedum]

@videlec this one is essenially ready. I need to make the documentation build again and fix some upstream issues but otherwise this is it.

I know this patch-bomb is not reviewable. I'd recommend to have a look at the news file to get a rough overview of what happened here: https://github.com/flatsurf/sage-flatsurf/pull/220/files#diff-a44f00f4a0a1ee8b0d4e68e5609335e17720b1d9b2ff039f6c74ce82cdcf5daa

The category setup is not incredibly elegant at times, e.g., to add something to oriented finite type half-translation surfaces without boundary, you have to put it in:

class HalfTranslationSurfaces:
    class Oriented:
        class FiniteType:
            class WithoutBoundary:
                class ParentMethods:
                    def stratum(self): …

We could flatten this somewhat (and work around how this is meant to be used by SageMath) but maybe this is good enough for the first iteration?

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Admittedly this went a bit too far maybe. The old sage-flatsurf had 40k LoC and this changeset contains +20k/-10k; it adds a lot of documentation actually ;)

[github-actions[bot]]

Documentation preview for this PR is ready! :tada: Built with commit: 03eef30ed60f44fa72360e9579b6a7c6988cc3ac