SystemParamBuilder - Enable type inference of closure parameter when building dynamic systems (#14820)

# Objective

When building a system from `SystemParamBuilder`s and defining the
system as a closure, the compiler should be able to infer the parameter
types from the builder types.

## Solution

Create methods for each arity that take an argument that implements both
`SystemParamFunction` as well as `FnMut(SystemParamItem<P>,...)`. The
explicit `FnMut` constraint will allow the compiler to infer the
necessary higher-ranked lifetimes along with the parameter types.

I wanted to show that this was possible, but I can't tell whether it's
worth the complexity. It requires a separate method for each arity,
which pollutes the docs a bit:
![SystemState build_system
docs](https://github.com/user-attachments/assets/5069b749-7ec7-47e3-a5e4-1a4c78129f78)

## Example

```rust
let system = (LocalBuilder(0u64), ParamBuilder::local::<u64>())
    .build_state(&mut world)
    .build_system(|a, b| *a + *b + 1);
```

crates/bevy_ecs/src/system/builder.rs

@@ -457,6 +457,21 @@ mod tests {
         assert_eq!(result, 3);
     }
 
+    #[test]
+    fn multi_param_builder_inference() {
+        let mut world = World::new();
+
+        world.spawn(A);
+        world.spawn_empty();
+
+        let system = (LocalBuilder(0u64), ParamBuilder::local::<u64>())
+            .build_state(&mut world)
+            .build_system(|a, b| *a + *b + 1);
+
+        let result = world.run_system_once(system);
+        assert_eq!(result, 1);
+    }
+
     #[test]
     fn param_set_builder() {
         let mut world = World::new();

crates/bevy_ecs/src/system/function_system.rs

@@ -208,6 +208,52 @@ pub struct SystemState<Param: SystemParam + 'static> {
     archetype_generation: ArchetypeGeneration,
 }
 
+// Allow closure arguments to be inferred.
+// For a closure to be used as a `SystemParamFunction`, it needs to be generic in any `'w` or `'s` lifetimes.
+// Rust will only infer a closure to be generic over lifetimes if it's passed to a function with a Fn constraint.
+// So, generate a function for each arity with an explicit `FnMut` constraint to enable higher-order lifetimes,
+// along with a regular `SystemParamFunction` constraint to allow the system to be built.
+macro_rules! impl_build_system {
+    ($($param: ident),*) => {
+        impl<$($param: SystemParam),*> SystemState<($($param,)*)> {
+            /// Create a [`FunctionSystem`] from a [`SystemState`].
+            /// This method signature allows type inference of closure parameters for a system with no input.
+            /// You can use [`SystemState::build_system_with_input()`] if you have input, or [`SystemState::build_any_system()`] if you don't need type inference.
+            pub fn build_system<
+                Out: 'static,
+                Marker,
+                F: FnMut($(SystemParamItem<$param>),*) -> Out
+                    + SystemParamFunction<Marker, Param = ($($param,)*), In = (), Out = Out>
+            >
+            (
+                self,
+                func: F,
+            ) -> FunctionSystem<Marker, F>
+            {
+                self.build_any_system(func)
+            }
+
+            /// Create a [`FunctionSystem`] from a [`SystemState`].
+            /// This method signature allows type inference of closure parameters for a system with input.
+            /// You can use [`SystemState::build_system()`] if you have no input, or [`SystemState::build_any_system()`] if you don't need type inference.
+            pub fn build_system_with_input<
+                Input,
+                Out: 'static,
+                Marker,
+                F: FnMut(In<Input>, $(SystemParamItem<$param>),*) -> Out
+                    + SystemParamFunction<Marker, Param = ($($param,)*), In = Input, Out = Out>,
+            >(
+                self,
+                func: F,
+            ) -> FunctionSystem<Marker, F> {
+                self.build_any_system(func)
+            }
+        }
+    }
+}
+
+all_tuples!(impl_build_system, 0, 16, P);
+
 impl<Param: SystemParam> SystemState<Param> {
     /// Creates a new [`SystemState`] with default state.
     ///
@@ -242,7 +288,9 @@ impl<Param: SystemParam> SystemState<Param> {
     }
 
     /// Create a [`FunctionSystem`] from a [`SystemState`].
-    pub fn build_system<Marker, F: SystemParamFunction<Marker, Param = Param>>(
+    /// This method signature allows any system function, but the compiler will not perform type inference on closure parameters.
+    /// You can use [`SystemState::build_system()`] or [`SystemState::build_system_with_input()`] to get type inference on parameters.
+    pub fn build_any_system<Marker, F: SystemParamFunction<Marker, Param = Param>>(
         self,
         func: F,
     ) -> FunctionSystem<Marker, F> {