Remove the 'Photo filter carousel' recipe

[antfitch]

Description of what this PR is changing or adding, and why:

Remove a recipe that references non-Flutter code.

Issues fixed by this PR (if any):

Fixes #8204

PRs or commits this PR depends on (if any):

n/a

Presubmit checklist

• This PR is marked as draft with an explanation if not meant to land until a future stable release.
• This PR doesn’t contain automatically generated corrections (Grammarly or similar).
• This PR follows the Google Developer Documentation Style Guidelines — for example, it doesn’t use i.e. or e.g., and it avoids I and we (first person).
• This PR uses semantic line breaks of 80 characters or fewer.

[flutter-website-bot]

Visit the preview URL for this PR (updated for commit 442e7e1):

https://flutter-docs-prod--pr11453-fw-8204-remove-recipe-ygynfeuc.web.app

[sfshaza2]

This PR looks great except for a couple things:

• We don't like broken links. So, after this PR lands, trying to access the page gives you a 404, as you can see in the staged version: https://flutter-docs-prod--pr11453-fw-8204-remove-recipe-ygynfeuc.web.app/cookbook/effects/photo-filter-carousel
  To address this, add a redirect to the firebase.json file at the top of the repo. You can redirect to the cookbook index.
• You shouldn't need to delete this from the index file. It's my understanding that this file is autogenerated. Right, @parlough? Or is that no longer the case?

Thanks, @antfitch!

[parlough]

You shouldn't need to delete this from the index file. It's my understanding that this file is autogenerated. Right, @parlough? Or is that no longer the case?

This index file is still manually built, I believe maybe because the automatic order based on name isn't exactly what we wanted. So it still needs to be removed.