Usage of scalar-leaf trees with multi-output objectives

In https://github.com/dmlc/xgboost/issues/12278 , it was mentioned:
> In one tree-per-class mode, one idea would be to recompute the gradients after each tree, instead of after each group of trees. This turns it into a coordinate descent algorithm which is much better at dealing with curvature.

Following this example:
https://xgboost.readthedocs.io/en/stable/tutorials/advanced_custom_obj.html

If setting parameters `num_boost_round=1` and `base_score=0` without any base_score, then calling something like:
```python
booster.inplace_predict(X, predict_type="margin")
```

I would expect from that comment and from the documentation to get a single tree making predictions for a single column of the output, but `.predict()` produces an output where each column has a non-zero value, even though the custom objective is called only once (verified by putting prints on it) and there is a single tree, as verified by:

```python
import json
trees = json.loads(booster.save_raw(raw_format="json"))["learner"]["gradient_booster"]["model"]["trees"]
len(trees)
```

What's happening there?

Start with the advanced custom objective documentation and the discussion in issue 12278. Reproduce the case with num_boost_round=1, base_score=0, inplace_predict(..., predict_type="margin"), and the JSON tree-count check, then trace why predict() returns non-zero values for every output column. Done means explaining whether this behavior is expected or identifying the change needed.

Written by the indexing model from the issue text.