Search records don't get deleted when related document is deleted

[TimLanzi]

Describe the Bug

When I delete a document that is synced with the search plugin, the search result document is still available.

Link to the code that reproduces this issue

N/A

Reproduction Steps

1. Use create-payload-app. Use website template and postgres database.
2. Create account and seed database.
3. Delete a Post.
4. Go to Search Results collection. Deleted post will still be in Search Results.

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

plugin: search

Environment Info

Binaries:
  Node: 22.7.0
  npm: 10.8.2
  Yarn: 1.22.22
  pnpm: 9.8.0
Relevant Packages:
  payload: 3.1.0
  next: 15.0.3
  @payloadcms/db-postgres: 3.1.0
  @payloadcms/email-nodemailer: 3.1.0
  @payloadcms/graphql: 3.1.0
  @payloadcms/live-preview: 3.1.0
  @payloadcms/live-preview-react: 3.1.0
  @payloadcms/next/utilities: 3.1.0
  @payloadcms/payload-cloud: 3.1.0
  @payloadcms/plugin-form-builder: 3.1.0
  @payloadcms/plugin-nested-docs: 3.1.0
  @payloadcms/plugin-redirects: 3.1.0
  @payloadcms/plugin-search: 3.1.0
  @payloadcms/plugin-seo: 3.1.0
  @payloadcms/richtext-lexical: 3.1.0
  @payloadcms/translations: 3.1.0
  @payloadcms/ui/shared: 3.1.0
  react: 19.0.0-rc-65a56d0e-20241020
  react-dom: 19.0.0-rc-65a56d0e-20241020
Operating System:
  Platform: linux
  Arch: x64
  Version: #202405300957~1732141768~22.04~f2697e1 SMP PREEMPT_DYNAMIC Wed N
  Available memory (MB): 31971
  Available CPU cores: 8