Roadmap for new R interface

ref https://github.com/dmlc/xgboost/issues/9734
ref https://github.com/dmlc/xgboost/issues/9475

This issue is intended as a roadmap tracker for progress in bringing xgboost's R interface up to date and discussions around these tasks and coordination.

From the previous tasks, here I've made a list of potential tasks to take on, but I might be missing some things, and I've put the biggest task (new `xgboost()` function) under a single bullet point while in practice it'll likely involve multiple rounds of PRs. Please feel free to add more tasks to this list.

I've taken the liberty of classifying these issues in terms of whether they'd be blockers for releasing a new xgboost version or not, albeit some people might disagree with my assessments.

* [x] (Blocker) Enable categorical features for current `DMatrix` constructors (`matrix`, `dgCMatrix`, `dgRMatrix`).
* [x] (Blocker) Add support for creating DMatrices from R `data.frame` objects, automatically setting `factor` variables to be of categorical type in the DMatrix. (#9828)
* Note: these objects are a list of arrays which aren't necessarily in a single memory chunk, and which can have types `int` (int32_t), `double` (float64), and potentially `int64_t` from package `bit64`.
* I guess this and the first point could be done in the same PR since they might be touching similar code sections.
* [x] (Blocker) Fix [plotting and trees-to-table with categorical splits](https://github.com/dmlc/xgboost/issues/9925).
* [x] Add `XGDMatrixNumNonMissing`.
* [x] Add `XGDMatrixGetDataAsCSR`.
* [x] (Blocker) Enable multi-output input labels and predictions.
* [ ] (Low priority) Add a mechanism to create a `DMatrix` object from `arrow` objects (from package "arrow"). Like for data frames, should automatically recognize categorical columns from the categorical arrow type.
* Note: the idea here is to exploit functions that work directly on arrow format, **without** converting to base R arrays (which do not support all the arrow types) along the way.
* [x] Add an interface to create `QuantileDMatrix` objects from R, accepting the same kinds of inputs as `DMatrix` (`data.frame`, `matrix`, `dgCMatrix`, `dgRMatrix`, `arrow` if implemented, maybe `float::float32`), and also auto-recognizing categorical features for objects that have them (data frames and arrow tables).
* [x] (Low priority) Add methods to get additional info from `DMatrix` objects that are currently missing from the R package, such as `get_quantile_cut` (guess this is just a call to `XGDMatrixGetQuantileCut`?).
* [x] (Blocker) Move more `DMatrix` parameters that reference data towards `xgb.DMatrix()` function arguments, such as `qid`, `group`, `label_lower_bound`, `label_upper_bound` , etc.
* Potentially a good reference could be the DMatrix [python class](https://github.com/dmlc/xgboost/blob/34a261669614e63c8095df1a01842e5920330b30/python-package/xgboost/core.py#L750).
* [x] Switch the current `DMatrix` creation function for R matrices towards the C function that uses `array_interface`.
* [x] Switch the `predict` method for the current booster to use "inplace predict" or other more efficient `DMatrix` creators when appropriate.
* [x] (Blocker) Remove all the public interface (functions, docs, tests, examples) around the `Booster.handle` class, as well as the conversion methods from handle to booster and vice-versa, leaving only the booster for now.
* [x] (Blocker) After the task above is done, switch the handle serialization mechanism to ALTREP and remove `xgb.Booster.complete`, which wouldn't be needed anymore.
* [x] This increases the R requirement to >= 4.3, so it requires modifying the CI jobs to update them all to this version of R and drop the older ones.
* ~(Low priority) Implement serialization for `DMatrix` handles through the same ALTREP system as above.~ This idea was discarded ([thread](https://github.com/dmlc/xgboost/issues/9734#issuecomment-1839914385))
* [x] (Blocker) Remove the current `xgboost()` function, and remove the calls from all the places it gets used (tests, examples, vignettes, etc.).
* [x] (Blocker) After support for `data.frame` and categorical features is added, then create a new `xgboost()` function from scratch that wouldn't share any code base with the current function named like that, ideally working as a higher-level wrapper over `DMatrix` + `xgb.train` but implementing the kind of idiomatic R interface (**x/y only, no formula**) described in [the earlier thread](https://github.com/dmlc/xgboost/issues/9734), either with a separate function for the parameters or everything being passed in the main function.
* It should return objects of a different class than `xgb.train` (perhaps the class could be named "xgboost").
* This class should have its own `predict` method, again with a different interface than the booster's predict, as described in the first message here.
* If this class needs to keep additional attributes, perhaps they could be kept as part of the JSON that gets serialized, otherwise should have a note about serialization and transferability with other interfaces.
* This is probably the largest PR in terms of code (especially tests!!), so might need to be split into different batches. For example, support for custom objectives could be left out from the first PR.
* [x] (Blocker) After the new `xgboost()` x/y interface gets implemented, then modify other functions to accept these objects - e.g.:
* Plotting function.
* Feature importance function.
* Serialization functions that are aimed at transferring models between interfaces.
* All of these should keep in mind small details like base-1 indexing for tree numbers and similar.
* [x] (Blocker) Create examples and vignettes for the new `xgboost()` function.
* [ ] (Low priority) Perhaps create a higher-level cv function for the new `xgboost()` interface.
* [x] Support creation of external memory objects with `DataIter`.
* [x] (Blocker) Enable quantile regression with multiple quantiles.
* [ ] Switch the R package build system to CMake instead of autotools.
* [ ] (Low priority) Distributed training, perhaps integration with RSpark.
* [ ] Documentation and unified tests for 1-based indexing.
* [x] (Blocker) Fix misrendered documentation: https://github.com/dmlc/xgboost/issues/10329
* [x] (Blocker) Update introductory vignette to reflect current XGBoost capabilities https://github.com/dmlc/xgboost/issues/10746