BUG: Series.str.replace/translate resulting dtype is different from pandas if an invalid pattern was passed

[dchigarev]

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Reproducible Example

import pandas
import modin.pandas as pd

pd_ser = pandas.Series(["a", "b", "ab"])
md_ser = pd.Series(["a", "b", "ab"])

md_res = md_ser.str.replace(pat=None, repl="some", regex=False)
pd_res = pd_ser.str.replace(pat=None, repl="some", regex=False)

print(f"modin dtypes:\n{md_res.dtypes}\n") # object
print(f"pandas dtypes:\n{pd_res.dtypes}\n") # float64

print(f"modin internal dtypes:\n{md_res._to_pandas().dtypes}") # float64 (doesn't match modin's cache)

Issue Description

Here we pass None as a pattern that produces a Series full of nans as the result (instead of expected Series of strings):

>>> pd.Series(["a", "b"]).str.replace(None, "b", regex=False)
0   NaN
1   NaN
dtype: float64

Modin can't infer new dtype dynamically and just copies it:

modin/modin/core/storage_formats/pandas/query_compiler.py

Line 1601 in 7a95be2

str_replace = Map.register(_str_map("replace"), dtypes="copy", shape_hint="column")

(Everything works well if the pattern is not None)

Expected Behavior

To match pandas behavior

Error Logs

Replace this line with the error backtrace (if applicable).

Installed Versions

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

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Note: this issue is part of an epic #3804