Static indicator shouldn't be shown when searchParams is being used

Link to the code that reproduces this issue

https://codesandbox.io/p/devbox/awesome-shockley-46z7c5

To Reproduce

1. Start the dev server
2. Create a new page and use searchParams

export default async function Page({
  searchParams,
}: {
  searchParams: Promise<{a: string}>;
}) {
  const sp = await searchParams;

  return (
    <div>
      <p>sp: {sp.a}</p>
    </div>
  );
}

3. Visit the page on the browser and the static indicator should not be shown here since searchParams is considered a Dynamic API

Build time:
In the build time process, though, the page is correctly rendered as a dynamic page (the /sp route):

Current vs. Expected behavior

The static indicator should not be shown here since searchParams is considered a Dynamic API.

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: 20.9.0
  npm: 9.8.1
  Yarn: 1.22.19
  pnpm: 8.10.2
Relevant Packages:
  next: 15.0.3-canary.2 // Latest available version is detected (15.0.3-canary.2).
  eslint-config-next: N/A
  react: 19.0.0-rc-603e6108-20241029
  react-dom: 19.0.0-rc-603e6108-20241029
  typescript: 5.3.3
Next.js Config:
  output: N/A

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

Developer Experience

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

next dev (local)

Additional context

No response

Start with the linked CodeSandbox and reproduce the behavior in next dev using a page that awaits searchParams. Then trace the next dev static indicator handling for Dynamic APIs and verify that the indicator is absent while the /sp route remains dynamic at build time.