[RFC] Modularize the tree class in both Python and Cython to enable easy extensions

### Describe the workflow you want to enable

As we are waiting for a reviewer to review #22754 , @thomasjpfan suggested we just move forward with our goals of creating a package of more exotic tree splits. E.g. https://arxiv.org/abs/1909.11799. While we wait for reviewers, the suggestion is to make a package within `scikit-learn-contrib`. 

Although we would like for #22754 to be eventually merged into scikit-learn, we understand reviewer backlog is an issue. To move forward while reviews occur, we would need to subclass existing scikit-learn code. Ideally, we would like to introduce minor refactoring changes that would make this task significantly easier.

We would like to subclass directly from scikit-learn without requiring us to keep an up-to-date fork of scikit-learn with all the bug fixes and maintenance that the dev team here does. We can limit this if we modularize the Python/Cython functions inside the `sklearn/tree` module.

### Describe your proposed solution

I am proposing two refactoring modifications that have no impact on the performance of the current tree estimators in scikit-learn.

1. Refactor the `BaseDecisionTree` Python class to have the following functions that can be overridden in a subclass:

- `_set_tree_class`: sets the Tree Cython class that the Python API uses
- `_set_splitter`: sets the Splitter Cython class that the Python API uses

For example, this makes the subclassing of BaseDecisionTree cleaner: https://github.com/scikit-learn/scikit-learn/blob/de06afa78458d773d7c0482ff17a55a235d0886b/sklearn/tree/_classes.py#L410-L416.

2. Refactor the `Tree` Cython class to have the following functions:

- `_set_node_values`: transfers split node values to the storage node
- `_compute_feature_value`: uses the storage node and the input data to compute the feature value to split on

For example, see https://github.com/scikit-learn/scikit-learn/blob/de06afa78458d773d7c0482ff17a55a235d0886b/sklearn/tree/_tree.pyx#L770-L787.

3. Refactor the `TreeBuilder` Cython class to pass around a `Split` pointer, rather than the struct itself

This will enable someone to use C-level functions to pass around another struct with a similar structure as `Split`.

For example, see https://github.com/scikit-learn/scikit-learn/blob/de06afa78458d773d7c0482ff17a55a235d0886b/sklearn/tree/_tree.pyx#L193.

### Describe alternatives you've considered, if relevant

Alternatives would require maintaining a copy of the `sklearn/tree` module and keep it up-to-date w/ sklearn changes. If this was just one Cython file, I would say it is possible, but the necessary ingredients span some of the underlying private API, making this a very time-consuming task. Introducing modularity into the private API that does not impact existing performance, therefore seems to be the best path forward?

Moreover, by introducing these refactoring changes, #22754 has a smaller diff and lower-cost to review.

### Additional context

**#22754 demonstrates that there is no performance regression, or issues w/ existing DecisionTree, or RandomForest when introducing these changes.**

COMMENT:
In general to summarize the points in this thread and others, private extension API is fine if:

1. documentation clearly states no stability
2. benchmarks against `main` demonstrate the trees do not lose performance in terms of runtime (accuracy is a given)
3. the introduced abstractions are not difficult to maintain and are not too complex

Lmk if I missed anything. 

> BTW as a work around, a third party library can pin scikit-learn as a build dependency to get the Cython tree code for a specific scikit-learn version. During runtime, their code can still work with newer versions of scikit-learn.

Yes this is a good point. It is actually what I ended up doing in [scikit-tree](https://github.com/neurodata/scikit-tree) by leveraging a forked-submodule of scikit-learn purely for the Cython tree code.

Labels: New Feature, module:ensemble, module:tree, cython, Needs Decision - Include Feature, Refactor