Change private watcher support call public and private if available

See https://github.com/Textualize/textual/pull/2442#issuecomment-1529512891

This changes the original PR so that, rather than calling a private watcher
instead of a public, as originally issued, we now call public and private,
if they're both there.

If they are both there private is called first.

src/textual/reactive.py

@@ -241,11 +241,13 @@ class Reactive(Generic[ReactiveType]):
                     events.Callback(callback=partial(await_watcher, watch_result))
                 )
 
-        watch_function = getattr(
-            obj, f"_watch_{name}", getattr(obj, f"watch_{name}", None)
-        )
-        if callable(watch_function):
-            invoke_watcher(watch_function, old_value, value)
+        private_watch_function = getattr(obj, f"_watch_{name}", None)
+        if callable(private_watch_function):
+            invoke_watcher(private_watch_function, old_value, value)
+
+        public_watch_function = getattr(obj, f"watch_{name}", None)
+        if callable(public_watch_function):
+            invoke_watcher(public_watch_function, old_value, value)
 
         # Process "global" watchers
         watchers: list[tuple[Reactable, Callable]]

tests/test_reactive.py

@@ -390,8 +390,8 @@ async def test_watch_compute():
     assert watch_called == [True, True, False, False, True, True, False, False]
 
 
-async def test_private_watch() -> None:
-    """A private watch method should win over a public watch method."""
+async def test_public_and_private_watch() -> None:
+    """If a reactive/var has public and private watches both should get called."""
 
     calls: dict[str, bool] = {"private": False, "public": False}
 
@@ -409,4 +409,4 @@ async def test_private_watch() -> None:
         assert calls["public"] is False
         pilot.app.counter += 1
         assert calls["private"] is True
-        assert calls["public"] is False
+        assert calls["public"] is True