[Bug]: `ax.transData` does not honor data limits

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### Bug summary

`ax.transData` does not honor `xlim` and `ylim`. The document at https://matplotlib.org/stable/users/explain/artists/transforms_tutorial.html#data-coordinates seems to suggest that data limits are updated automatically when new data are added to the axes, but it's not the case, which breaks `ax.transData`, since it reads an old version of data limits.

### Code for reproduction

```Python
from matplotlib import pyplot as plt

fig, ax = plt.subplots(figsize=(10, 10), dpi=100)
print(f"fig size: {fig.get_size_inches() * fig.dpi}")

ax.plot([0, 10], [0, 10], 'o')

print(f"(10, 10) in data coordinates: {ax.transData.transform((10, 10))}")

ax.set_xlim(ax.get_xlim()) # just ax.get_xlim() or ax.viewLim or ax.autoscale_view() is enough
ax.set_ylim(ax.get_ylim())

print(f"(10, 10) in data coordinates: {ax.transData.transform((10, 10))}")
```

### Actual outcome

fig size: [1000. 1000.]
(10, 10) in data coordinates: [7875. 7810.]
(10, 10) in data coordinates: [864.77272727 845. ]

### Expected outcome

fig size: [1000. 1000.]
(10, 10) in data coordinates: [864.77272727 845. ]
(10, 10) in data coordinates: [864.77272727 845. ]

### Additional information

The wording from https://matplotlib.org/stable/users/explain/artists/transforms_tutorial.html#data-coordinates suggests that data limits are updated automatically when new data are added, but it requires manual trigger of `set_xlim`/`set_ylim` (or `get_xlim`/`get_ylim` which calls `ax.viewLim`).

This is quite confusing. I would hope that either the documentation is updated to notify the user to explicitly update the data limits, or even better, let `transData`/`transLimits` always use the latest data limits.

### Operating system

_No response_

### Matplotlib Version

3.8.3

### Matplotlib Backend

_No response_

### Python version

_No response_

### Jupyter version

_No response_

### Installation

None

Reproduce the provided snippet, then inspect the transData/transLimits update path and the linked data-coordinates documentation. Determine whether the resolution is a code change or documentation clarification, and verify the example's coordinate output after the chosen change.

Written by the indexing model from the issue text.