diff --git a/homeassistant/components/http/ban.py b/homeassistant/components/http/ban.py
index eec951fb907..b4e949514b8 100644
--- a/homeassistant/components/http/ban.py
+++ b/homeassistant/components/http/ban.py
@@ -116,7 +116,8 @@ async def process_wrong_login(request: Request) -> None:
     """
     hass = request.app[KEY_HASS]
 
-    remote_addr = ip_address(request.remote)  # type: ignore[arg-type]
+    assert request.remote
+    remote_addr = ip_address(request.remote)
     remote_host = request.remote
     with suppress(herror):
         remote_host, _, _ = await hass.async_add_executor_job(
diff --git a/homeassistant/components/meteo_france/__init__.py b/homeassistant/components/meteo_france/__init__.py
index e43572ade6c..ddba982934c 100644
--- a/homeassistant/components/meteo_france/__init__.py
+++ b/homeassistant/components/meteo_france/__init__.py
@@ -54,6 +54,7 @@ async def async_setup_entry(hass: HomeAssistant, entry: ConfigEntry) -> bool:
 
     async def _async_update_data_alert() -> CurrentPhenomenons:
         """Fetch data from API endpoint."""
+        assert isinstance(department, str)
         return await hass.async_add_executor_job(
             client.get_warning_current_phenomenoms, department, 0, True
         )
diff --git a/homeassistant/core.py b/homeassistant/core.py
index cdf5cbfe6a8..533bddb6ceb 100644
--- a/homeassistant/core.py
+++ b/homeassistant/core.py
@@ -40,6 +40,7 @@ from typing import (
     ParamSpec,
     Self,
     TypedDict,
+    TypeVarTuple,
     cast,
     overload,
 )
@@ -135,6 +136,7 @@ _T = TypeVar("_T")
 _R = TypeVar("_R")
 _R_co = TypeVar("_R_co", covariant=True)
 _P = ParamSpec("_P")
+_Ts = TypeVarTuple("_Ts")
 # Internal; not helpers.typing.UNDEFINED due to circular dependency
 _UNDEF: dict[Any, Any] = {}
 _CallableT = TypeVar("_CallableT", bound=Callable[..., Any])
@@ -529,7 +531,7 @@ class HomeAssistant:
         self.bus.async_fire(EVENT_HOMEASSISTANT_STARTED)
 
     def add_job(
-        self, target: Callable[..., Any] | Coroutine[Any, Any, Any], *args: Any
+        self, target: Callable[[*_Ts], Any] | Coroutine[Any, Any, Any], *args: *_Ts
     ) -> None:
         """Add a job to be executed by the event loop or by an executor.
 
@@ -547,7 +549,7 @@ class HomeAssistant:
             )
             return
         if TYPE_CHECKING:
-            target = cast(Callable[..., Any], target)
+            target = cast(Callable[[*_Ts], Any], target)
         self.loop.call_soon_threadsafe(
             functools.partial(
                 self.async_add_hass_job, HassJob(target), *args, eager_start=True
@@ -558,8 +560,8 @@ class HomeAssistant:
     @callback
     def async_add_job(
         self,
-        target: Callable[..., Coroutine[Any, Any, _R]],
-        *args: Any,
+        target: Callable[[*_Ts], Coroutine[Any, Any, _R]],
+        *args: *_Ts,
         eager_start: bool = False,
     ) -> asyncio.Future[_R] | None:
         ...
@@ -568,8 +570,8 @@ class HomeAssistant:
     @callback
     def async_add_job(
         self,
-        target: Callable[..., Coroutine[Any, Any, _R] | _R],
-        *args: Any,
+        target: Callable[[*_Ts], Coroutine[Any, Any, _R] | _R],
+        *args: *_Ts,
         eager_start: bool = False,
     ) -> asyncio.Future[_R] | None:
         ...
@@ -587,8 +589,9 @@ class HomeAssistant:
     @callback
     def async_add_job(
         self,
-        target: Callable[..., Coroutine[Any, Any, _R] | _R] | Coroutine[Any, Any, _R],
-        *args: Any,
+        target: Callable[[*_Ts], Coroutine[Any, Any, _R] | _R]
+        | Coroutine[Any, Any, _R],
+        *args: *_Ts,
         eager_start: bool = False,
     ) -> asyncio.Future[_R] | None:
         """Add a job to be executed by the event loop or by an executor.
@@ -623,7 +626,7 @@ class HomeAssistant:
         # the type used for the cast. For history see:
         # https://github.com/home-assistant/core/pull/71960
         if TYPE_CHECKING:
-            target = cast(Callable[..., Coroutine[Any, Any, _R] | _R], target)
+            target = cast(Callable[[*_Ts], Coroutine[Any, Any, _R] | _R], target)
         return self.async_add_hass_job(HassJob(target), *args, eager_start=eager_start)
 
     @overload
@@ -772,7 +775,7 @@ class HomeAssistant:
 
     @callback
     def async_add_executor_job(
-        self, target: Callable[..., _T], *args: Any
+        self, target: Callable[[*_Ts], _T], *args: *_Ts
     ) -> asyncio.Future[_T]:
         """Add an executor job from within the event loop."""
         task = self.loop.run_in_executor(None, target, *args)
@@ -783,7 +786,7 @@ class HomeAssistant:
 
     @callback
     def async_add_import_executor_job(
-        self, target: Callable[..., _T], *args: Any
+        self, target: Callable[[*_Ts], _T], *args: *_Ts
     ) -> asyncio.Future[_T]:
         """Add an import executor job from within the event loop."""
         task = self.loop.run_in_executor(self.import_executor, target, *args)
@@ -844,14 +847,14 @@ class HomeAssistant:
     @overload
     @callback
     def async_run_job(
-        self, target: Callable[..., Coroutine[Any, Any, _R]], *args: Any
+        self, target: Callable[[*_Ts], Coroutine[Any, Any, _R]], *args: *_Ts
     ) -> asyncio.Future[_R] | None:
         ...
 
     @overload
     @callback
     def async_run_job(
-        self, target: Callable[..., Coroutine[Any, Any, _R] | _R], *args: Any
+        self, target: Callable[[*_Ts], Coroutine[Any, Any, _R] | _R], *args: *_Ts
     ) -> asyncio.Future[_R] | None:
         ...
 
@@ -865,8 +868,9 @@ class HomeAssistant:
     @callback
     def async_run_job(
         self,
-        target: Callable[..., Coroutine[Any, Any, _R] | _R] | Coroutine[Any, Any, _R],
-        *args: Any,
+        target: Callable[[*_Ts], Coroutine[Any, Any, _R] | _R]
+        | Coroutine[Any, Any, _R],
+        *args: *_Ts,
     ) -> asyncio.Future[_R] | None:
         """Run a job from within the event loop.
 
@@ -894,7 +898,7 @@ class HomeAssistant:
         # the type used for the cast. For history see:
         # https://github.com/home-assistant/core/pull/71960
         if TYPE_CHECKING:
-            target = cast(Callable[..., Coroutine[Any, Any, _R] | _R], target)
+            target = cast(Callable[[*_Ts], Coroutine[Any, Any, _R] | _R], target)
         return self.async_run_hass_job(HassJob(target), *args)
 
     def block_till_done(self) -> None: