BUG: Interpolate over time does not work with Int64 or Float64
- [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
pd.DataFrame({"a": [1, None, 2]}, index=pd.to_datetime([1,2,3], unit="d")).convert_dtypes().interpolate(method="time")
```

```
Traceback (most recent call last):
  File "C:\venv\lib\site-packages\IPython\core\interactiveshell.py", line 3437, in run_code
    exec(code_obj, self.user_global_ns, self.user_ns)
  File "<ipython-input-7-4eba02001155>", line 1, in <module>
    pd.DataFrame({"a": [1, None, 2]}, index=pd.to_datetime([1,2,3], unit="d")).convert_dtypes().interpolate(method="time")
  File "C:\venv\lib\site-packages\pandas\core\generic.py", line 7222, in interpolate
    new_data = obj._mgr.interpolate(
  File "C:\venv\lib\site-packages\pandas\core\internals\managers.py", line 593, in interpolate
    return self.apply("interpolate", **kwargs)
  File "C:\venv\lib\site-packages\pandas\core\internals\managers.py", line 427, in apply
    applied = getattr(b, f)(**kwargs)
  File "C:\venv\lib\site-packages\pandas\core\internals\blocks.py", line 1931, in interpolate
    values=values.fillna(value=fill_value, method=method, limit=limit),
  File "C:\venv\lib\site-packages\pandas\core\arrays\base.py", line 655, in fillna
    value, method = validate_fillna_kwargs(value, method)
  File "C:\venv\lib\site-packages\pandas\util\_validators.py", line 367, in validate_fillna_kwargs
    method = clean_fill_method(method)
  File "C:\venv\lib\site-packages\pandas\core\missing.py", line 82, in clean_fill_method
    raise ValueError(f"Invalid fill method. Expecting {expecting}. Got {method}")

ValueError: Invalid fill method. Expecting pad (ffill) or backfill (bfill). Got time

```

#### Problem description

Without the `convert_dtypes()` this works without any problems.

#### Expected Output

```
              a
1970-01-02  1.0
1970-01-03  1.5
1970-01-04  2.0
```


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

<details>

INSTALLED VERSIONS
------------------
commit           : f2c8480af2f25efdbd803218b9d87980f416563e
python           : 3.8.7.final.0
python-bits      : 64
OS               : Windows
OS-release       : 10
Version          : 10.0.18362
machine          : AMD64
processor        : Intel64 Family 6 Model 142 Stepping 12, GenuineIntel
byteorder        : little
LC_ALL           : None
LANG             : None
LOCALE           : English
pandas           : 1.2.3
numpy            : 1.19.5
pytz             : 2021.1
dateutil         : 2.8.1
pip              : 21.0.1
setuptools       : 49.2.1
Cython           : None
pytest           : 6.2.2
hypothesis       : None
sphinx           : None
blosc            : None
feather          : None
xlsxwriter       : None
lxml.etree       : None
html5lib         : None
pymysql          : None
psycopg2         : None
jinja2           : 2.11.3
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          : 3.0.0
pyxlsb           : None
s3fs             : None
scipy            : 1.6.1
sqlalchemy       : None
tables           : None
tabulate         : None
xarray           : None
xlrd             : None
xlwt             : None
numba            : None

</details>
