[BUG]: px.sunburst / px.treemap / px.icicle with path give a different sector order on every run for Polars DataFrames

Start in plotly/express/_core.py at process_dataframe_hierarchy and trace the group_by calls used for path-based charts. Compare the Polars, pandas, and PyArrow hierarchy ordering, then inspect the regression test included or proposed by the reporter. Done means repeated Polars runs produce stable, first-appearance ordering consistent with the other supported inputs.

Description

When path= is used with a Polars DataFrame, px.sunburst, px.treemap and px.icicle build their ids / labels / parents / values arrays in a different order every time the script is run. The same data as a pandas DataFrame or a PyArrow table always gives the same order: the order in which the sectors first appear in the data.

The cause is in process_dataframe_hierarchy (plotly/express/_core.py). Each level of the hierarchy is built with df.group_by(path[i:]).agg(...). With pandas (narwhals uses sort=False) and PyArrow the groups come back in order of first appearance, but Polars' group_by does not guarantee any order, so the order of the output changes from run to run.

Consequences:

• fig.to_json() / fig.write_html() output is not reproducible with Polars input (snapshot tests, caching, diffs of generated HTML).
• With sort=False, or when sectors have equal values, the chart itself is laid out differently on each run.
• Polars results differ from pandas / PyArrow results for identical data.

Screenshots/Video

N/A: the difference is in the figure data; see the output below.

Steps to reproduce

import plotly
import plotly.express as px
import polars as pl

df = pl.DataFrame(
    {
        "region": ["South", "North", "South", "West", "North", "West"],
        "sector": ["Tech", "Finance", "Finance", "Tech", "Tech", "Finance"],
        "sales": [1, 2, 3, 4, 5, 6],
    }
)
fig = px.sunburst(df, path=["region", "sector"], values="sales")
print(plotly.__version__, pl.__version__, list(fig.data[0].ids))

Running the script three times (plotly 7.1.0, polars 1.44.2):

7.1.0 1.44.2 ['West/Tech', 'West/Finance', 'North/Finance', 'South/Finance', 'North/Tech', 'South/Tech', 'South', 'North', 'West']
7.1.0 1.44.2 ['South/Tech', 'West/Tech', 'North/Tech', 'South/Finance', 'North/Finance', 'West/Finance', 'West', 'North', 'South']
7.1.0 1.44.2 ['South/Tech', 'West/Tech', 'North/Tech', 'North/Finance', 'South/Finance', 'West/Finance', 'West', 'South', 'North']

With pd.DataFrame(...) instead, every run prints:

['South/Tech', 'North/Finance', 'South/Finance', 'West/Tech', 'North/Tech', 'West/Finance', 'South', 'North', 'West']

Notes

I have a small fix with a regression test and will open a PR for it.