Which issue does this PR close?

Part of #22555. This is PR 1 of 2 — see the issue body for the full plan. PR 2 will audit direct with_new_children callers and add a clippy lint.

Rationale for this change

Today the "skip work when children are unchanged" intent is split across two layers:

• caller-side — with_new_children_if_necessary short-circuits via Arc::ptr_eq on child pointers.
• callee-side — the check_if_same_properties! macro from Cache PlanProperties, add fast-path for with_new_children #19792, invoked inside each impl's with_new_children, short-circuits when children's PlanProperties Arcs match (allowing the plan to reuse its cached PlanProperties Arc instead of recomputing).

Having two independent layers means two places to maintain and two places for future changes to drift apart. This PR consolidates the fast-path into the single free-function helper so callers get both short-circuits uniformly.

What changes are included in this PR?

with_new_children_if_necessary now applies three layers, cheapest first:

1. Same child pointers — every children[i] is Arc::ptr_eq to the corresponding existing child → return the original plan unchanged, no allocation.
2. Same child properties — children's PlanProperties Arcs match → call the new ExecutionPlan::with_new_children_and_same_properties trait method to reuse the plan's PlanProperties cache without recomputing.
3. Full recompute — otherwise, delegate to ExecutionPlan::with_new_children.

To make layer 2 dispatchable via &dyn ExecutionPlan, with_new_children_and_same_properties is promoted from an ad-hoc inherent method on each impl to a trait method with a safe default that falls back to with_new_children. All 22 existing impls migrate their inherent method to a trait override (mechanical change — signature &self → self: Arc<Self>, return Self → Result<Arc<dyn ExecutionPlan>>, body wrapped in Ok(Arc::new(...))).

The check_if_same_properties! macro and its call sites inside impls are kept, so direct callers of with_new_children (which PR 2 will audit + migrate) do not regress on this PR.

Are these changes tested?

Yes — added test_with_new_children_if_necessary_layers in execution_plan.rs that constructs test-local WithChildrenTestLeaf + WithChildrenTestParent plans (the parent tracks recompute vs fast-path calls via AtomicUsize) and asserts, for each of the three layers:

• Layer 1: Arc::ptr_eq(result, parent) returns true, recompute_calls == 0, fast_path_calls == 0
• Layer 2: Arc::ptr_eq(result.properties(), orig_props) returns true, recompute_calls == 0, fast_path_calls == 1
• Layer 3: Arc::ptr_eq(result.properties(), orig_props) returns false, recompute_calls == 1, fast_path_calls unchanged

All 1523 datafusion-physical-plan unit tests pass. Full workspace cargo check + cargo clippy --all-targets --all-features -- -D warnings pass.

Are there any user-facing changes?

Yes — ExecutionPlan gains a new default-implemented trait method with_new_children_and_same_properties. Downstream impls that used to override the ad-hoc inherent method with the same name will need to re-implement as a trait override (mechanical signature change). Marking as api change.

Follow-up (PR 2, not in this PR)

• Audit the ~47 remaining direct callers of plan.with_new_children(children) across the codebase and route them through with_new_children_if_necessary.
• Add a disallowed_methods clippy lint (or custom lint) that forbids direct ExecutionPlan::with_new_children outside of a small allow-list.
• Once all callers migrate, remove the check_if_same_properties! macro and its impl-side invocations, making the helper the single source of truth as described in the issue.