Router duplicates base path when using pages with shared parent in both page and app router

Link to the code that reproduces this issue

https://github.com/gabrielricardourbina/nextjs-route-bug

To Reproduce

Have pages with a shared parent in both Page and App router and having a basePath
For example

.
├── pages
│   └── parent
│       └── [parentId]
│           └── child
│               ├── [childId]
│               │   └── grand-child
│               │       └── [grandChildId].tsx
│               └── [childId].tsx
└── src
    └── app
        └── parent
            └── [parentId]
                └── page.tsx

Where parent is shared in both routers

Current vs. Expected behavior

Case A from App Router to Page Router ✅

Navigating from parent/[parentId] to parent/[parentId]/child/[child] or parent/[parentId]/child/[child]/grand-child/[grandChildId], results in the respective pages being rendered and the url matching the folder structure with the basePath being prepended correctly

Case B from Page Router to App Router ✅

Navigating from parent/[parentId]/child/[child] or parent/[parentId]/child/[child]/grand-child/[grandChildId] to parent/[parentId], results the page being rendered and the url matching the folder structure with the basePath being prepended correctly

Case C from Page Router to Page Router ❌

Navigating from parent/[parentId]/child/[child] to parent/[parentId]/child/[child]/grand-child/[grandChildId] or from parent/[parentId]/child/[child]/grand-child/[grandChildId] to parent/[parentId]/child/[child], results in a redirection to a non-existing page where the basePath is duplicated I.E. /base/base/*

Video

https://github.com/user-attachments/assets/3b990434-6166-4e5d-8c2f-8d0e284bf9c4

Provide environment information

Operating System:
  Platform: darwin
  Arch: arm64
  Version: Darwin Kernel Version 24.2.0: Fri Dec  6 18:51:28 PST 2024; root:xnu-11215.61.5~2/RELEASE_ARM64_T8112
  Available memory (MB): 24576
  Available CPU cores: 8
Binaries:
  Node: 18.20.2
  npm: 9.9.4
  Yarn: N/A
  pnpm: N/A
Relevant Packages:
  next: 15.1.6 // Latest available version is detected (15.1.6).
  eslint-config-next: 14.2.23
  react: 19.0.0
  react-dom: 19.0.0
  typescript: 5.7.3
Next.js Config:
  output: N/A

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

Not sure, Pages Router, Dynamic Routes, Linking and Navigating, Redirects

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

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

Additional context

No response

Start with the linked reproduction and its pages/ and src/app/ route trees, using the shared parent, dynamic segments, and basePath described in the issue. Exercise navigation between the Page Router child and grand-child routes, then trace the routing and redirect entry points involved. Done means both directions resolve to the expected route without duplicating the base path.