Keep a live Pick or Omit class view's identity when it flows into another structural type

A Pick or Omit view of a program class that holds the instance (its view
exposes a method) now carries the class's identity in the flow analysis,
and its values count as instances of that class. Assigning such a view
to another structural type keeps the instance, so reads through the
second type see the instance's later writes instead of a copy's.

packages/compiler/src/frontend/lowering/class-protocols.ts

@@ -414,6 +414,11 @@ export class ClassProtocols {
         for (const part of ts.constituentTypes(type)) add(part);
         return;
       }
+      // A Pick or Omit view's values are instances of the class it views.
+      if (this.pickOfProgramClass(type)) {
+        add(type.getAliasTypeArguments()[0]!);
+        return;
+      }
       const symbol = type.getSymbol();
       if (symbol === undefined) return;
       if (this.isProgramClassInstance(type)) {
@@ -603,6 +608,8 @@ export class ClassProtocols {
       return element !== undefined && this.carriesIdentity(element, marked);
     }
     if (this.isProgramClassInstance(type)) return true;
+    // A live Pick or Omit view of a program class holds the instance itself.
+    if (this.pickOfProgramClass(type) && this.usesCheckedIdentity(type)) return true;
     const symbol = type.getSymbol();
     if (symbol === undefined) return false;
     if (marked.has(symbol)) return true;

tests/corpus/6414-pick-class-method-views.ts

@@ -37,3 +37,19 @@ void run({ client, name: "ctx" }).then(() => {
   finish(client);
   console.log(count(client), client.calls);
 });
+
+// A live view that flows into another structural type keeps the instance:
+// reads through the second view see the instance's later writes.
+interface Counter {
+  calls: number;
+}
+function counted(view: Pick<ApiClient, "request" | "calls">): Counter {
+  void view.request("/z");
+  return view;
+}
+const second = new ApiClient("https://k");
+const counter = counted(second);
+second.calls += 10;
+const holder: { counter: Counter } = { counter: counted(second) };
+second.calls = 100;
+console.log("counter", counter.calls, holder.counter.calls, second.calls);