BUG: Don't ignore errors when casting dtype in Series constructor

[snitish]

• closes BUG: pd.Series fails to cast datetime series containing only NaT to timedelta type #60728
• Tests added and passed if fixing a bug or adding a new feature
• All code checks passed.
• Added type annotations to new arguments/methods/functions.
• Added an entry in the latest doc/source/whatsnew/vX.X.X.rst file if fixing a bug or adding a new feature.

In the constructor for Series, when the input data is another Series with a different dtype than the one specified in the constructor, the dtype conversion currently doesn't throw errors and silently sets the wrong dtype.

>>> example = pd.Series(
...     pd.Series([pd.NaT], dtype="datetime64[ns]"), dtype="timedelta64[ns]"
... )
>>> print(example.dtype)
datetime64[ns]

[mroeschke]

Thanks again @snitish

[rhshadrach]

With this PR, this now raises:

pd.Series([1.5], dtype="int64")

While perhaps we want to do this in the future, I think it can have a large impact and we definitely should not do it without proper deprecation. Ref: #60728 (comment)

[rhshadrach]

Ah, ignore me, that line always raised. I confused it with

pd.Series(pd.Series([1.5], dtype="float64"), dtype="int64")

which still gives int64 dtype as before.