`"rest_after_insert_{$enabled_post_type}"` actions are set too early, `duplicate_post_enabled_post_types` filter has no effect.

• I've searched for any related issues and avoided creating a duplicate issue.

Please give us a description of what happened

The "rest_after_insert_{$enabled_post_type}" actions are added too early, there is no way to add a duplicate_post_enabled_post_types filter before them.
The solution would be to add these actions in init action or similar, so these lines would be executed in init: https://github.com/Yoast/duplicate-post/blob/trunk/src/post-republisher.php#L48-L55

This would give the themes/plugins chance to register duplicate_post_enabled_post_types filter before the REST hooks.

To Reproduce

Step-by-step reproduction instructions

1. Add duplicate_post_enabled_post_types filter in your theme or plugin.
2. Observe that "rest_after_insert_{$enabled_post_type}" action is registered only for post types from the settings not including ones added through duplicate_post_enabled_post_types filter.

Expected results

1. The duplicate_post_enabled_post_types should allow to set custom post types that can be then used to add "rest_after_insert_{$enabled_post_type}" actions.

Actual results

1. The "rest_after_insert_{$enabled_post_type}" actions are set before the theme or plugin has a chance to set duplicate_post_enabled_post_types filter.
2. This results in An error occurred while deleting the Rewrite & Republish copy. error when you try to duplicate custom post type set in duplicate_post_enabled_post_types filter.

Screenshots, screen recording, code snippet

I get this error when I try to rewrite & republish a custom post type added through filter duplicate_post_enabled_post_types:

Technical info

• If relevant, which editor is affected (or editors):

• Block Editor
• Gutenberg Editor
• Classic Editor
• Other:

• Which browser is affected (or browsers):

• Chrome
• Firefox
• [x ] Safari
• Opera

Used versions

• Device you are using: PC
• Operating system: Windows 10
• PHP version: 8.2
• WordPress version: 6.5.5
• WordPress Theme: Twenty-Twenty
• Yoast Duplicate Post version: 4.5
• Gutenberg plugin version:
• Classic Editor plugin version:
• Relevant plugins in case of a bug: none

Open src/post-republisher.php around lines 48-55 and trace when the REST actions are registered relative to the duplicate_post_enabled_post_types filter. Reproduce the custom post-type case described in the issue, then verify that the filtered post type receives the expected REST action and no longer produces the deletion error.