Can't reindex search when using next's basePath option

[suphon-t]

Describe the Bug

The reindex button from the search plugin calls incorrect URL when using Next's basePath option.

In this picture, I've set the basePath to /payload, so API routes are under /payload/api, but the reindex button calls /api without the prefix, causing it to return 404.

Link to the code that reproduces this issue

https://github.com/suphon-t/payload/tree/reproduce/search-reindex-next-basepath

Reproduction Steps

1. Create a new project using npx create-payload-app
2. Edit next.config.mjs and set basePath to something (in this case, I set it to /payload)
3. Open the admin panel and go to the "Search Results" collection
4. Reindex any collection
5. The button calls an incorrect URL and gets a 404

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

plugin: search

Environment Info

Binaries:
  Node: 22.12.0
  npm: 10.9.0
  Yarn: N/A
  pnpm: 9.15.1
Relevant Packages:
  payload: 3.15.1
  next: 15.1.0
  @payloadcms/email-nodemailer: 3.15.1
  @payloadcms/graphql: 3.15.1
  @payloadcms/next/utilities: 3.15.1
  @payloadcms/payload-cloud: 3.15.1
  @payloadcms/plugin-search: 3.15.1
  @payloadcms/richtext-lexical: 3.15.1
  @payloadcms/translations: 3.15.1
  @payloadcms/ui/shared: 3.15.1
  react: 19.0.0
  react-dom: 19.0.0
Operating System:
  Platform: darwin
  Arch: arm64
  Version: Darwin Kernel Version 24.2.0: Fri Dec  6 18:56:34 PST 2024; root:xnu-11215.61.5~2/RELEASE_ARM64_T6020
  Available memory (MB): 65536
  Available CPU cores: 12

Note that I'm using v3.15.1 because v3.16.0 - v3.17.1 currently suffers from #10534.