BUG: KeyError from unexpected DatetimeIndex partial str indexing
- [x] I have checked that this issue has not already been reported.

- [x] I have confirmed this bug exists on the latest version of pandas.

- [ ] (optional) I have confirmed this bug exists on the master branch of pandas.

---


#### Code Sample, a copy-pastable example

```python
import pandas as pd
df = pd.DataFrame({'a': [0, 1]}, index=[pd.Timestamp('2002-12-30T20'), pd.Timestamp('2003-01-03T20')])
df['T 1.75 1/3'] = [1, 2]
```

#### Problem description

When using `__setitem__` or `__getitem__` with a str key on a pandas DataFrame where the index has ._supports_partial_string_indexing = True, pandas first tries to convert the str key to a slice using index._get_string_slice(key).

It seems to me that we have too loose of an interpretation of what one of these partial string slices looks like (or perhaps when / how one might use them).

In my use case I have some timeseries data for some US treasury bills, where the names are something like f"T {coupon} {date}", e.g. "T 1.75 1/3" and I want to assign a new column to a DataFrame with some data on this instrument.
However `df['T 1.75 1/3'] = value` - as in the example above - raises "ValueError: cannot set using a slice indexer with a different length than the value"

#### Expected Output

A new column with label "T 1.75 1/3" and values [1, 2] is assigned to the pandas DataFrame `df`.

#### Output of ``pd.show_versions()``

<details>

INSTALLED VERSIONS
------------------
commit           : f2c8480af2f25efdbd803218b9d87980f416563e
python           : 3.9.2.final.0
python-bits      : 64
OS               : Linux
OS-release       : 4.19.128-microsoft-standard
Version          : #1 SMP Tue Jun 23 12:58:10 UTC 2020
machine          : x86_64
processor        :
byteorder        : little
LC_ALL           : None
LANG             : C.UTF-8
LOCALE           : en_US.UTF-8

pandas           : 1.2.3
numpy            : 1.20.1
pytz             : 2021.1
dateutil         : 2.8.1
pip              : 21.0.1
setuptools       : 53.0.0
Cython           : None
pytest           : None
hypothesis       : None
sphinx           : None
blosc            : None
feather          : None
xlsxwriter       : None
lxml.etree       : None
html5lib         : None
pymysql          : None
psycopg2         : None
jinja2           : None
IPython          : 7.21.0
pandas_datareader: None
bs4              : None
bottleneck       : None
fsspec           : None
fastparquet      : None
gcsfs            : None
matplotlib       : None
numexpr          : None
odfpy            : None
openpyxl         : None
pandas_gbq       : None
pyarrow          : None
pyxlsb           : None
s3fs             : None
scipy            : None
sqlalchemy       : None
tables           : None
tabulate         : None
xarray           : None
xlrd             : None
xlwt             : None
numba            : None

</details>
