fix(demo): the setup flow's baseline writes are allowlisted

A demo visitor who typed a height on the confirm screen got a 403 and a
generic toast, and the "someone I look after" arm could only take
"Finish without the profile": the profile PUT, the self-context PUT and
the managed-profile POST were missing from the demo allowlist, so only
the empty-form path completed.

All three are added, pinned per method as the rest of the list is. None
of them creates health data.

src/__tests__/proxy-demo-mode-allowlist.test.ts

@@ -106,6 +106,36 @@ describe("proxy.ts DEMO_MODE mutation allowlist", () => {
     expect(missing, "onboarding writes the demo cannot make").toEqual([]);
   });
 
+  it("permits the baseline writes the confirm screen makes (M-m)", () => {
+    // v1.39 (Wave C, C6) — a demo visitor who typed a height got a 403 and a
+    // generic toast, and "someone I look after" could only take "Finish
+    // without the profile": the three writes the confirm screen makes were
+    // not on the list. None of them is health data — the account's own
+    // profile fields, the encrypted self-context the anamnesis card writes,
+    // and the managed record the flow's guardian arm creates.
+    for (const [path, method] of [
+      ["/api/auth/profile", "PUT"],
+      ["/api/coach/about-me", "PUT"],
+      ["/api/managed-profiles", "POST"],
+    ] as const) {
+      expect(
+        proxy(makeRequest(path, method)).status,
+        `${method} ${path} is blocked in the demo`,
+      ).not.toBe(403);
+    }
+  });
+
+  it("does not drag in a sibling verb on the baseline paths", () => {
+    expect(proxy(makeRequest("/api/auth/profile", "DELETE")).status).toBe(403);
+    expect(proxy(makeRequest("/api/managed-profiles", "DELETE")).status).toBe(
+      403,
+    );
+    // The per-profile routes are a different path and stay closed.
+    expect(
+      proxy(makeRequest("/api/managed-profiles/abc", "DELETE")).status,
+    ).toBe(403);
+  });
+
   it("still blocks a health-data mutation (POST /api/measurements)", () => {
     const res = proxy(makeRequest("/api/measurements", "POST"));
     expect(res.status).toBe(403);

src/proxy.ts

@@ -174,6 +174,19 @@ const DEMO_MUTATION_ALLOWLIST: ReadonlyArray<{ path: string; method: string }> =
     // Neither creates health data.
     { path: "/api/onboarding/disclaimer", method: "POST" },
     { path: "/api/onboarding/tour", method: "POST" },
+    // v1.39 (Wave C, C6) — the three writes the confirm screen makes. Without
+    // them a demo visitor who typed a height got a 403 and a generic toast,
+    // and the "someone I look after" arm could only take "Finish without the
+    // profile" — only the empty-form/Skip path completed, so the demo did not
+    // in fact walk the same flow (design spec §Principles 5). None of the
+    // three creates health data: the caller's own profile fields, the
+    // encrypted self-context behind the optional anamnesis card, and the
+    // managed record the guardian arm of the flow exists to create. The
+    // per-profile routes (`/api/managed-profiles/{id}`, its guardians) are
+    // different paths and stay closed.
+    { path: "/api/auth/profile", method: "PUT" },
+    { path: "/api/coach/about-me", method: "PUT" },
+    { path: "/api/managed-profiles", method: "POST" },
   ];
 
 // Legacy route redirects (German → English)