BUG: memory issues with `string[pyarrow]` after sorted `pd.merge`

[noahblakesmith]

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 random
import string

import pandas as pd
import pyarrow as pa

# Gen random data ----------------------------------------------------------------------

random.seed(42)
txt = "".join(random.choices(string.printable, k=int(1e4)))
num = random.choices(range(int(1e6)), k=int(125e3))

# Gen dataframes -----------------------------------------------------------------------

a = pd.Series(num, dtype="Int64")
b = pd.Series([txt] * int(125e3), dtype="string[pyarrow]")

lhs = pd.DataFrame({"a": a, "b": b})
# Concatenation is necessary to reproduce bug (not sure why)
lhs = pd.concat([lhs, lhs], ignore_index=True, verify_integrity=True)

rhs = pd.DataFrame({"a": a}).drop_duplicates()

# Merge with and without sorting -------------------------------------------------------

df_nosort = pd.merge(left=lhs, right=rhs, on="a", sort=False)
print(df_nosort.memory_usage(deep=True))

df_sort = pd.merge(left=lhs, right=rhs, on="a", sort=True)
print(df_sort.memory_usage(deep=True))

# `b` cols are equal despite memory usage difference
print(df_nosort["b"].equals(df_sort["b"]))

# Write to parquet files ---------------------------------------------------------------

schema = pa.schema([pa.field("a", pa.int64()), pa.field("b", pa.string())])

df_nosort.to_parquet("df_nosort.parquet", schema=schema)
df_sort.to_parquet("df_sort.parquet", schema=schema)

Issue Description

Issues only occur when series b has dtype of string[pyarrow] (not string[python]).

1. .to_parquet fails for df_sort but succeeds for df_nosort.
2. The memory usage of b is greater in df_sort than in df_nosort.
3. Despite differences in memory usage, df_sort["b"] is equal to df_nosort["b"].

Expected Behavior

1. I would expect .to_parquet to succeed for both dataframes.
2. I would expect df_sort["b"] to have the same memory usage as df_nosort["b"]. (I should note, however, that I lack a sophisticated understanding of memory management, so I may be mistaken.)
3. I would expect df_nosort["b"].equals(df_sort["b"]) to return False if the series differ in memory usage. (Same caveat applies.)

Installed Versions

INSTALLED VERSIONS

commit : 0691c5c
python : 3.10.16
python-bits : 64
OS : Darwin
OS-release : 24.4.0
Version : Darwin Kernel Version 24.4.0: Wed Mar 19 21:16:34 PDT 2025; root:xnu-11417.101.15~1/RELEASE_ARM64_T6000
machine : arm64
processor : arm
byteorder : little
LC_ALL : None
LANG : en_US.UTF-8
LOCALE : en_US.UTF-8

pandas : 2.2.3
numpy : 2.2.2
pytz : 2025.2
dateutil : 2.9.0.post0
pip : 25.0
Cython : None
sphinx : None
IPython : 8.35.0
adbc-driver-postgresql: None
adbc-driver-sqlite : None
bs4 : 4.13.3
blosc : None
bottleneck : None
dataframe-api-compat : None
fastparquet : None
fsspec : 2025.3.2
html5lib : None
hypothesis : None
gcsfs : None
jinja2 : 3.1.6
lxml.etree : 5.3.1
matplotlib : None
numba : None
numexpr : None
odfpy : None
openpyxl : 3.1.5
pandas_gbq : None
psycopg2 : None
pymysql : None
pyarrow : 19.0.1
pyreadstat : None
pytest : None
python-calamine : None
pyxlsb : None
s3fs : None
scipy : None
sqlalchemy : 2.0.39
tables : None
tabulate : None
xarray : None
xlrd : 2.0.1
xlsxwriter : None
zstandard : None
tzdata : 2025.2
qtpy : None
pyqt5 : None

[arjuanwall]

take

[bingbhakdibhumi]

take

[phiofuni]

take

[eenkhbol]

take

[rhshadrach]

I'm seeing similar behavior as the other issue: #61316 (comment)