`use cache: private` not working during client-side navigation

Link to the code that reproduces this issue

https://github.com/ajaykarthikr/next-16-use-cache-private-bug

To Reproduce

1. Create a cached function with "use cache: private" that uses cookies():

   // lib/user.ts
   import { cookies } from "next/headers";
   import { cacheTag, cacheLife } from "next/cache";
   
   export async function getUser() {
       "use cache: private";
       cacheTag(`userdata`);
       cacheLife({ stale: 30 });
       
       const sessionId = (await cookies()).get('session-id')?.value || 'guest'
       
       console.log("Fetching user data"); // This logs on every navigation
       await new Promise((resolve) => setTimeout(resolve, 5000));
       const timestamp = new Date().toISOString();
   
       return {
           user: {
               name: "Ajay",
               email: "ajay@example.com"
           },
           timestamp: timestamp,
       }
   }
   

2. Use this function in a Server Component page:

   // app/about/page.tsx
   import { Suspense } from "react";
   import { getUser } from "../../lib/user";
   
   export default async function Page() {
       return (
           <div>
               <h1>About Page</h1>
               <Suspense fallback={<p>Loading...</p>}>
                   <Content />
               </Suspense>
           </div>
       )
   }
   
   async function Content() {
       const data = await getUser();
       return (
           <div>
               <h1>{data.user.name}</h1>
               <p>Fetched at: {data.timestamp}</p>
           </div>
       );
   }
   

3. Configure next.config.ts:

   import type { NextConfig } from "next";
   
   const nextConfig: NextConfig = {
   cacheComponents: true,
   };
   
   export default nextConfig;
   

4. Navigate to the page (e.g., /about), then navigate away, then navigate back using client-side navigation (using component)

Current vs. Expected behavior

Expected: The cached function should return the cached result during the 30-second stale period, showing the same timestamp and not logging "Fetching user data" on subsequent navigations.

Actual: The function re-executes on every client-side navigation, showing a new timestamp each time and logging "Fetching user data" in the console.

Demo: https://next-16-use-cache-private-bug.vercel.app/

Provide environment information

Operating System:
  Platform: darwin
  Arch: arm64
  Version: Darwin Kernel Version 25.0.0: Wed Sep 17 21:42:08 PDT 2025; root:xnu-12377.1.9~141/RELEASE_ARM64_T8132
  Available memory (MB): 24576
  Available CPU cores: 10
Binaries:
  Node: 22.20.0
  npm: 10.9.3
  Yarn: N/A
  pnpm: N/A
Relevant Packages:
  next: 16.0.2-canary.3 // Latest available version is detected (16.0.2-canary.3).
  eslint-config-next: N/A
  react: 19.2.0
  react-dom: 19.2.0
  typescript: 5.9.3
Next.js Config:
  output: N/A

Which area(s) are affected? (Select all that apply)

Use Cache

Which stage(s) are affected? (Select all that apply)

next start (local), Vercel (Deployed)

Additional context

• The "use cache: private" directive is supposed to work with cookies() API according to the documentation
• This appears to be related to Router Cache interaction with function-level caching during client-side navigation
• The 2-second artificial delay in the reproduction makes it easy to observe when the function re-executes

Start with the linked reproduction, especially lib/user.ts, app/about/page.tsx, and next.config.ts. Run it with client-side navigation and compare the timestamp and “Fetching user data” log across revisits. Done means the private cached function reuses its result during the 30-second stale period instead of executing on every navigation.