perf(aws-lambda): warm the audio function while the plan runs (#6148)

* perf(aws-lambda): warm the audio function while the plan runs

The audio task runs on the x86 render function, which is cold when the plan ran on the arm64 video function. A fire-and-forget invoke at the start of a render now wakes it, so the audio no longer outlasts the chunks.

* perf(aws-lambda): warm the render function only on a stack with a video function

An x86-only stack has no cold function to warm, so it takes the old path with no extra step. The CDK stack has no video function and is unchanged.

* perf(aws-lambda): wrap a template comment

* style(aws-lambda): format the warm-up template test

examples/aws-lambda/template.yaml

@@ -254,6 +254,11 @@ Resources:
           SelectPlanProtocol:
             Type: Choice
             Choices:
+              # Only a stack with the arm64 video function has a cold x86 function to warm.
+              # Without one the compared value can never match.
+              - Variable: $.PlanProtocol
+                StringEquals: !If [HasVideoFunction, v2, v2-without-video-function]
+                Next: WarmRender
               - Variable: $.PlanProtocol
                 StringEquals: v2
                 Next: PlanV2
@@ -265,6 +270,23 @@ Resources:
                 Next: UnsupportedPlanProtocol
             Default: PlanV2
 
+          # The audio task runs on this function once the plan is done; starting its container now hides the cold start.
+          WarmRender:
+            Type: Task
+            Resource: arn:aws:states:::lambda:invoke
+            Parameters:
+              FunctionName: !GetAtt RenderFunction.Arn
+              InvocationType: Event
+              Payload:
+                Action: warm
+            ResultPath: null
+            Catch:
+              - ErrorEquals:
+                  - States.ALL
+                ResultPath: null
+                Next: PlanV2
+            Next: PlanV2
+
           UnsupportedPlanProtocol:
             Type: Fail
             Error: PLAN_PROTOCOL_UNSUPPORTED