Simplify generic decorators in recorder (#125301)

* Simplify generic decorators in recorder

* Remove additional case

homeassistant/components/recorder/util.py

@@ -644,7 +644,7 @@ def _is_retryable_error(instance: Recorder, err: OperationalError) -> bool:
     )
 
 
-type _FuncType[_T, **_P, _R] = Callable[Concatenate[_T, _P], _R]
+type _FuncType[**P, R] = Callable[Concatenate[Recorder, P], R]
 type _FuncOrMethType[**_P, _R] = Callable[_P, _R]
 
 
@@ -683,9 +683,9 @@ def wrapper(*args: _P.args, **kwargs: _P.kwargs) -> bool:
     return decorator
 
 
-def database_job_retry_wrapper[_RecorderT: Recorder, **_P](
+def database_job_retry_wrapper[**_P](
     description: str, attempts: int = 5
-) -> Callable[[_FuncType[_RecorderT, _P, None]], _FuncType[_RecorderT, _P, None]]:
+) -> Callable[[_FuncType[_P, None]], _FuncType[_P, None]]:
     """Try to execute a database job multiple times.
 
     This wrapper handles InnoDB deadlocks and lock timeouts.
@@ -695,10 +695,10 @@ def database_job_retry_wrapper[_RecorderT: Recorder, **_P](
     """
 
     def decorator(
-        job: _FuncType[_RecorderT, _P, None],
-    ) -> _FuncType[_RecorderT, _P, None]:
+        job: _FuncType[_P, None],
+    ) -> _FuncType[_P, None]:
         @functools.wraps(job)
-        def wrapper(instance: _RecorderT, *args: _P.args, **kwargs: _P.kwargs) -> None:
+        def wrapper(instance: Recorder, *args: _P.args, **kwargs: _P.kwargs) -> None:
             for attempt in range(attempts):
                 try:
                     job(instance, *args, **kwargs)