perf: cache .schema and .columns for lazy-only backends

[MarcoGorelli]

See #2064 for context

For Dask / PySpark / DuckDB / polars.LazyFrame, we should probably cache schema and column names

Some guidelines:

First, do not do this for eager backends, because those may allow in-place operations which modify the data type. Example:

In [49]: df_pd = pd.DataFrame({'a':[1,1,2], 'b': [4,5,6]})

In [50]: df = nw.from_native(df)

In [51]: df.schema
Out[51]: Schema([('a', Int64), ('b', Int64)])

In [52]: df
Out[52]:
┌──────────────────┐
|Narwhals DataFrame|
|------------------|
|        a  b      |
|     0  1  4      |
|     1  1  5      |
|     2  2  6      |
└──────────────────┘

In [53]: df.schema
Out[53]: Schema([('a', Int64), ('b', Int64)])

In [54]: df_native = df.to_native()

In [55]: df_native.loc['a', 0] = 1.5

In [56]: df
Out[56]:
┌──────────────────┐
|Narwhals DataFrame|
|------------------|
|      a    b    0 |
| 0  1.0  4.0  NaN |
| 1  1.0  5.0  NaN |
| 2  2.0  6.0  NaN |
| a  NaN  NaN  1.5 |
└──────────────────┘

In [57]: df.schema
Out[57]: Schema([('a', Float64), ('b', Float64), (0, Float64)])

Is this poor design on pandas' part? Arguably. But, it's just what we've got to deal with.

Second, careful about using lru_cache on properties: https://youtu.be/sVjtp6tGo0g

[dangotbanned]

It is a bit hidden on here (https://arrow.apache.org/docs/python/data.html#arrays)

Arrow data is immutable, so values can be selected but not assigned.

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Second, careful about using lru_cache on properties: youtu.be/sVjtp6tGo0g

@MarcoGorelli functools.cached_property would be preferred for this case I assume?