Improve __new__ and __init__ precedence

[hauntsaninja]

Fixes #5647

See also #5642

This PR is incomplete as it currently stands. We need to do something cleverer that handles the full constructor chain. See also: https://typing.readthedocs.io/en/latest/spec/constructors.html

Probably shouldn't merge, but maybe if we chose to tie break with __new__ only if the return type of __new__ is not a subtype of the type being constructed, this would unambiguously be a step in the right direction.

[github-actions]

Diff from mypy_primer, showing the effect of this PR on open source code:

prefect (https://github.com/PrefectHQ/prefect)
- src/prefect/utilities/hashing.py:74: error: Argument 1 to "dumps" of "Serializer" has incompatible type "tuple[tuple[Any, ...], dict[str, Any]]"; expected "D"  [arg-type]
- src/prefect/results.py:942: error: Argument 1 has incompatible type "R@create_result"; expected "R@BaseResult"  [arg-type]
- src/prefect/results.py:1253: note: "_cache_object" of "BaseResult" defined here
- src/prefect/results.py:1449: error: Unexpected keyword argument "storage_block" for "_cache_object" of "BaseResult"  [call-arg]
- src/prefect/results.py:1449: error: Unexpected keyword argument "serializer" for "_cache_object" of "BaseResult"  [call-arg]
+ src/prefect/records/result_store.py:65: error: Unexpected keyword argument "_sync" for "write" of "PersistedResult"  [call-arg]
+ src/prefect/records/result_store.py:65: error: Value of type "Coroutine[Any, Any, R?]" must be used  [unused-coroutine]
+ src/prefect/records/result_store.py:65: note: Are you missing an await?
- src/prefect/logging/formatters.py:65: error: Argument 1 to "dumps" of "Serializer" has incompatible type "dict[str, Any]"; expected "D"  [arg-type]

rclip (https://github.com/yurijmikhalevich/rclip)
+ rclip/main.py:118: error: Need type annotation for "pbar"  [var-annotated]

beartype (https://github.com/beartype/beartype)
+ beartype/_check/error/errget.py:581: error: Unused "type: ignore" comment  [unused-ignore]

scrapy (https://github.com/scrapy/scrapy)
+ scrapy/utils/datatypes.py:94: error: Unused "type: ignore" comment  [unused-ignore]

mongo-python-driver (https://github.com/mongodb/mongo-python-driver)
+ bson/dbref.py:98: error: Need type annotation for "doc"  [var-annotated]