Pages router: Using `shallow` "push/replace" with proxy/middleware rewrites, results in rendering previous route

Link to the code that reproduces this issue

https://codesandbox.io/p/devbox/thirsty-bas-d3cdjr

To Reproduce

1. You require a proxy.ts / middleware.ts that rewrites the current route. In the example we have a device parameter, which includes the current type of device derived from the user agent.
2. Have at least 2 routes. The issue occurs if you navigate e.g. from the homepage to the /some-route example.
3. Have a shallow route transition to your own route, e.g. by updating query parameters
4. Execute the route push multiple times
5. You will end up on the previous route (in this case home). The address bar still shows the correct url though.

There is a workaround that worked until 15.4.0, but does not work anymore starting from at least 15.5.x (I did not yet test all the point releases in between). I'm not even sure if the "workaround" is a bug or this is how it is suppose to work.

Current vs. Expected behavior

Pushing shallow route updates multiple times should not render the previous route.

Provide environment information

Operating System:
  Platform: linux
  Arch: x64
  Version: #1 SMP PREEMPT_DYNAMIC Sun Aug  6 20:05:33 UTC 2023
  Available memory (MB): 4102
  Available CPU cores: 2
Binaries:
  Node: 20.12.1
  npm: 10.5.0
  Yarn: 1.22.19
  pnpm: 8.15.6
Relevant Packages:
  next: 16.0.3 // Latest available version is detected (16.0.3).
  eslint-config-next: N/A
  react: 18.3.1
  react-dom: 18.3.1
  typescript: 5.9.3
Next.js Config:
  output: N/A

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

Pages Router

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

next dev (local), next build (local), next start (local), Other (Deployed)

Additional context

The issue is reproducible down to next.js 14.

Start with the linked CodeSandbox and reproduce the issue using proxy.ts or middleware.ts rewrites, two routes, and repeated shallow query-parameter updates. Compare behavior across the reported Next.js versions, including 15.4.0 and 15.5.x. Done means repeated shallow push or replace operations continue rendering the current route rather than the previous route while the address bar remains correct.