BUG: wide_to_long fails/works depending on whether id variable is string/object

[MichaelTiemannOSC]

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

import pandas as pd

df = pd.DataFrame({'id':['id1', 'id2'], 'nullcol':[pd.NA, 777], 'a-1':[1, 11], 'a-2':[2, 22], 'a-3':[3, 33]})

# This works when ID is an object                                                                                                                                        
print(df.dtypes)
print(pd.wide_to_long(df, ['a', 'b'], i='id', j='num', sep='-', suffix='\d'))

df.id= df.id.astype('string')

# This fails when ID is an object                                                                                                                                        
print(df.dtypes)
print(pd.wide_to_long(df, ['a', 'b'], i='id', j='num', sep='-', suffix='\d'))

Issue Description

The wide_to_long function fails to transform a dataframe that has an id variable of type string, failing with this error message:

ValueError: No objects to concatenate

Expected Behavior

I would expect wide_to_long to behave identically, whether the id variable is of type string or type object. Unless the documentation specifically stated that only type object is supported.

Installed Versions

I am running Pandas 1.4.1, but because once upon a time I tried to install a development environment to create a pull request, I'm being forever punished by my unforgiving OSX environment:

import pandas as pd
pd.show_versions()
Traceback (most recent call last):
File "", line 1, in
File "/Users/michael/opt/miniconda3/envs/jupyter/lib/python3.10/site-packages/pandas/util/_print_versions.py", line 109, in show_versions
deps = _get_dependency_info()
File "/Users/michael/opt/miniconda3/envs/jupyter/lib/python3.10/site-packages/pandas/util/_print_versions.py", line 88, in _get_dependency_info
mod = import_optional_dependency(modname, errors="ignore")
File "/Users/michael/opt/miniconda3/envs/jupyter/lib/python3.10/site-packages/pandas/compat/_optional.py", line 126, in import_optional_dependency
module = importlib.import_module(name)
File "/Users/michael/opt/miniconda3/envs/jupyter/lib/python3.10/importlib/init.py", line 126, in import_module
return _bootstrap._gcd_import(name[level:], package, level)
File "", line 1050, in _gcd_import
File "", line 1027, in _find_and_load
File "", line 1006, in _find_and_load_unlocked
File "", line 688, in _load_unlocked
File "", line 883, in exec_module
File "", line 241, in _call_with_frames_removed
File "/Users/michael/opt/miniconda3/envs/jupyter/lib/python3.10/site-packages/setuptools/init.py", line 8, in
import _distutils_hack.override # noqa: F401
File "/Users/michael/opt/miniconda3/envs/jupyter/lib/python3.10/site-packages/_distutils_hack/override.py", line 1, in
import('_distutils_hack').do_override()
File "/Users/michael/opt/miniconda3/envs/jupyter/lib/python3.10/site-packages/_distutils_hack/init.py", line 71, in do_override
ensure_local_distutils()
File "/Users/michael/opt/miniconda3/envs/jupyter/lib/python3.10/site-packages/_distutils_hack/init.py", line 59, in ensure_local_distutils
assert '_distutils' in core.file, core.file
AssertionError: /Users/michael/opt/miniconda3/envs/jupyter/lib/python3.10/distutils/core.py

(jupyter) iMac-Pro:Downloads michael$ conda list | grep pandas
pandas                    1.4.0           py310hdd25497_0    conda-forge
pint-pandas               0.2                pyhd8ed1ab_0    conda-forge

[samukweku]

@MichaelTiemannOSC just as an addition, if you are picking this up; maybe pd.wide_to_long can also be rewritten to be more performant