### What changes were proposed in this pull request?
Make `astype` method data-type-based.
**Non-goal: Match pandas' `astype` TypeErrors.**
Currently, `astype` throws TypeError error messages only when the destination type is not recognized. However, for some destination types that don't make sense to the specific type of Series/Index, for example, `numeric Series/Index → bytes`, we don't have proper TypeError error messages.
Since the goal of the PR is refactoring mainly, the above issue might be resolved later if needed.
### Why are the changes needed?
There are many type checks in the `astype` method. Since `DataTypeOps` and its subclasses are introduced, we should refactor `astype` to make it data-type-based. In this way, code is cleaner, more maintainable, and more flexible.
### Does this PR introduce _any_ user-facing change?
No.
### How was this patch tested?
Unit tests.
Closes#32847 from xinrong-databricks/datatypeops_astype.
Authored-by: Xinrong Meng <xinrong.meng@databricks.com>
Signed-off-by: Takuya UESHIN <ueshin@databricks.com>
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