BUG: `na_rep` not respected in `to_*` methods with `pd.NA`

[mroeschke]

Pandas version checks

• I have checked that this issue has not already been reported.

• I have confirmed this bug exists on the latest version of pandas.

• I have confirmed this bug exists on the main branch of pandas.

Reproducible Example

In [13]: import pandas as pd

In [14]: df = pd.DataFrame([1, pd.NA], dtype="Int64")

In [15]: df.to_string(na_rep="foo")
Out[15]: '      0\n0     1\n1  <NA>'

In [16]: df.to_xml(na_rep="foo")
--> 283 raise TypeError(f"Invalid value '{str(value)}' for dtype {self.dtype}")

TypeError: Invalid value 'foo' for dtype Int64

Issue Description

Since these should output textual representations of the data, I would expect pd.NA to be replaced with a string na_rep

Expected Behavior

Since these should output textual representations of the data, I would expect pd.NA to be replaced with a string na_rep

Installed Versions

Replace this line with the output of pd.show_versions()

[rsm-23]

Want to look into this. So taking it for now.

[rsm-23]

take

[rsm-23]

@mroeschke shouldn't the representation for pd.NA be 'NaN' instead of <NA>?