BUG: interpolate not respecting copy_on_write

[phofl]

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

pd.options.mode.copy_on_write = True
df = DataFrame({"a": [1, np.nan, 3]})
view = df[:]
df.interpolate(inplace=True)

Issue Description

view should not get modified

     a
0  1.0
1  2.0
2  3.0

same problem for ffill, bfill, pad and backfill

Expected Behavior

     a
0  1.0
1  np.nan
2  3.0

Installed Versions

INSTALLED VERSIONS

commit : 948bf6d
python : 3.8.15.final.0
python-bits : 64
OS : Darwin
OS-release : 22.3.0
Version : Darwin Kernel Version 22.3.0: Thu Jan 5 20:50:21 PST 2023; root:xnu-8792.81.2~2/RELEASE_ARM64_T8112
machine : arm64
processor : arm
byteorder : little
LC_ALL : None
LANG : None
LOCALE : None.UTF-8

pandas : 2.0.0.dev0+1388.g948bf6d069
numpy : 1.23.5
pytz : 2022.7
dateutil : 2.8.2
setuptools : 65.6.3
pip : 22.3.1
Cython : 0.29.32
pytest : 7.2.0
hypothesis : 6.61.0
sphinx : 4.5.0
blosc : None
feather : None
xlsxwriter : 3.0.5
lxml.etree : 4.9.2
html5lib : 1.1
pymysql : 1.0.2
psycopg2 : 2.9.3
jinja2 : 3.1.2
IPython : 8.8.0
pandas_datareader: None
bs4 : 4.11.1
bottleneck : 1.3.5
brotli :
fastparquet : 2022.12.0
fsspec : 2022.11.0
gcsfs : 2022.11.0
matplotlib : 3.6.2
numba : 0.56.4
numexpr : 2.8.3
odfpy : None
openpyxl : 3.0.10
pandas_gbq : None
pyarrow : 10.0.1
pyreadstat : 1.2.0
pyxlsb : 1.0.10
s3fs : 2022.11.0
scipy : 1.9.3
snappy :
sqlalchemy : 1.4.46
tables : 3.7.0
tabulate : 0.9.0
xarray : 2022.12.0
xlrd : 2.0.1
zstandard : 0.19.0
tzdata : None
qtpy : None
pyqt5 : None
None

[lithomas1]

In #49473, interpolate was not implemented, so I wouldn't expect this to work ATM.

I can have a look at this if you're not already working on this.

[phofl]

#49473 is about removing unnecessary eager copies (I added interpolate and friends yesterday). Basically optimisations that become available through CoW.

This one is about interpolate and friends not respecting CoW, e.g. mutating more than one object. Meaning, this is a "must" fix for 2.0 while the optimisations are just nice to have right now.

[phofl]

opened a quick pr to make copies when necessary.