Satisfy Mypy for Livy Hook (#46157)

The Livy Hook shows ... strange MyPy errors and hard to say why.

First of all it incorrectly used multiple inheritance (BaseHook
already inherist from LoggingMixin) but then it seems that mypy
has been lost when it comes to fields available in the hook.
Setting them directly (like it happens in other hooks deriving
from HttpHook solves the MyPy issues.

providers/src/airflow/providers/apache/livy/hooks/livy.py

@@ -32,7 +32,6 @@
 
 from airflow.exceptions import AirflowException
 from airflow.providers.http.hooks.http import HttpAsyncHook, HttpHook
-from airflow.utils.log.logging_mixin import LoggingMixin
 
 if TYPE_CHECKING:
     from airflow.models import Connection
@@ -53,7 +52,7 @@ class BatchState(Enum):
     SUCCESS = "success"
 
 
-class LivyHook(HttpHook, LoggingMixin):
+class LivyHook(HttpHook):
     """
     Hook for Apache Livy through the REST API.
 
@@ -88,7 +87,9 @@ def __init__(
         extra_headers: dict[str, Any] | None = None,
         auth_type: Any | None = None,
     ) -> None:
-        super().__init__(http_conn_id=livy_conn_id)
+        super().__init__()
+        self.method = "POST"
+        self.http_conn_id = livy_conn_id
         self.extra_headers = extra_headers or {}
         self.extra_options = extra_options or {}
         if auth_type:
@@ -457,7 +458,7 @@ def _validate_extra_conf(conf: dict[Any, Any]) -> bool:
         return True
 
 
-class LivyAsyncHook(HttpAsyncHook, LoggingMixin):
+class LivyAsyncHook(HttpAsyncHook):
     """
     Hook for Apache Livy through the REST API asynchronously.
 
@@ -490,7 +491,9 @@ def __init__(
         extra_options: dict[str, Any] | None = None,
         extra_headers: dict[str, Any] | None = None,
     ) -> None:
-        super().__init__(http_conn_id=livy_conn_id)
+        super().__init__()
+        self.method = "POST"
+        self.http_conn_id = livy_conn_id
         self.extra_headers = extra_headers or {}
         self.extra_options = extra_options or {}