Fix/empty string datetimelike conversion/issue 36550
- [x] xref #36550
- [x] tests added / passed
- [x] passes `black pandas`
- [x] passes `git diff upstream/master -u -- "*.py" | flake8 --diff`
- [ ] whatsnew entry

# Empty string conversion

The actual comportment of Timedelta, Timestamp and to_datetime is to return NaT.
```python
import pandas as pd
pd.to_datetime("", errors="raise")
# NaT
pd.to_datetime("", errors="coerce")
# NaT
pd.to_datetime("", errors="ignore")
# NaT
pd.Timedelta("")
# NaT
pd.Timestamp("")
# NaT
```

I would propose to raise a ValueError instead, same as for string that are not datetimelike, as follow:

 ```python
import pandas as pd
import pytest

with pytest.raises(ValueError):
    pd.to_datetime("", errors="raise")
pd.to_datetime("", errors="coerce")
# NaT
pd.to_datetime("", errors="ignore")
# ''

with pytest.raises(ValueError):
    pd.Timedelta("")
with pytest.raises(ValueError):
    pd.Timestamp("")
```

# Tests

I added the relevant test for the expected comportment.
I still will have to fix some test that rely on the current behaviors.

# Benchmark

I ran the following command
`asv continuous -E virtualenv -f 1.1 upstream/master HEAD -b "^tslibs.(timestamp|timedelta|tslib)"`
<details>

```
       before           after         ratio
     [8f6ec1e8]       [4393cc9e]
     <master>         <fix/empty-string-datetimelike-conversion/issue-36550>
+         173±1ns         202±10ns     1.17  tslibs.timestamp.TimestampProperties.time_is_leap_year(tzlocal(), 'B')
+         162±2ns          188±4ns     1.16  tslibs.timestamp.TimestampProperties.time_is_quarter_start(tzlocal(), None)
+         178±1ns         205±20ns     1.15  tslibs.timestamp.TimestampProperties.time_dayofweek(tzfile('/usr/share/zoneinfo/US/Central'), 'B')
+         163±2ns         186±10ns     1.15  tslibs.timestamp.TimestampProperties.time_is_year_end(tzlocal(), None)
+         162±1ns         185±10ns     1.15  tslibs.timestamp.TimestampProperties.time_is_year_end(tzfile('/usr/share/zoneinfo/US/Central'), None)
+         162±2ns         185±10ns     1.14  tslibs.timestamp.TimestampProperties.time_is_year_end(<UTC>, None)
+         169±2ns         193±10ns     1.14  tslibs.timestamp.TimestampProperties.time_is_quarter_end(tzlocal(), None)
+         164±2ns          186±4ns     1.14  tslibs.timestamp.TimestampProperties.time_is_quarter_start(tzutc(), None)
+     4.60±0.03μs       5.16±0.3μs     1.12  tslibs.timestamp.TimestampProperties.time_is_year_end(datetime.timezone(datetime.timedelta(seconds=3600)), 'B')
+         147±1ns          163±4ns     1.11  tslibs.timestamp.TimestampProperties.time_microsecond(<DstTzInfo 'Europe/Amsterdam' LMT+0:20:00 STD>, 'B')
+         170±2ns          188±7ns     1.11  tslibs.timestamp.TimestampProperties.time_is_quarter_end(tzfile('/usr/share/zoneinfo/US/Central'), None)
+       179±0.7ns         197±10ns     1.10  tslibs.timestamp.TimestampProperties.time_dayofweek(datetime.timezone(datetime.timedelta(seconds=3600)), None)
+       174±0.3ns         191±10ns     1.10  tslibs.timestamp.TimestampProperties.time_is_leap_year(<DstTzInfo 'Europe/Amsterdam' LMT+0:20:00 STD>, 'B')

SOME BENCHMARKS HAVE CHANGED SIGNIFICANTLY.
PERFORMANCE DECREASED.
```
</details>

why this change? likely to break test parsing generally and would have to see a lot of benefit Considering empty string equivalent to NaT as a huge influence on all method that try to cast data into datetimelike (happen in groupby, merge, join, equal, probably others methods)
Globaly, I think we should refrain from **implicit** conversion of string to datetimelike, and this PR goes one step in this direction.
An other issue related to mixing string and datetimelike can be found here #36545 

For information the broken test were the following:
```
pandas/tests/io/parser/test_parse_dates.py::test_parse_dates_empty_string[c_high]
pandas/tests/io/parser/test_parse_dates.py::test_parse_dates_empty_string[c_low]
pandas/tests/io/parser/test_parse_dates.py::test_parse_dates_empty_string[python]
pandas/tests/plotting/test_datetimelike.py::TestTSPlot::test_ts_plot_with_tz['UTC']
pandas/tests/tools/test_to_datetime.py::TestToDatetimeMisc::test_to_datetime_types[True]
pandas/tests/tools/test_to_datetime.py::TestToDatetimeMisc::test_to_datetime_types[False]
pandas/tests/tools/test_to_timedelta.py::TestTimedeltas::test_to_timedelta
```

If empty string should be always considered as NaT, then I'll close this PR.

 does this actually close the referenced issue? can you merge master Closing for now. @nrebena let us know if you'd like to start this up again and we'll reopen