Items not indexed immediately with workbench moderation on

Thanks for creating this issue report!
While I appreciate that this might cause a problem in rare cases, I'm unsure whether this really warrants that additional code and complexity. It does seem like a rather "edgy" edge case – and with such code, there's always the possibility of now running into a different edge case.
So, thanks, but unless more people come out here in support of fixing this, I don't think I'll be committing this.

So, thanks, but unless more people come out here in support of fixing this, I don't think I'll be committing this.

I think the problem applies only in specific scenarios.
We had this with search_api_et + workbench_moderation, and this site still has an older version of the latter. Not sure if the same would happen in a newer version.

Normally, without search_api_et, it would go like this:
If we look in node_save():

• hook_node_update() runs first, here workbench_moderation registers its shutdown function.
• hook_entity_update() runs after that, here search_api registers its shutdown function.

So the shutdown function from search_api would run after workbench_moderation, which is good.

But with search_api_et and entity_translation, we get this when a translation is saved:
Again, in hook_node_save():

• hook_field_attach_update() runs first, here the translations are saved. From here, hook_entity_translation_update() is called, and from there search_api_et calls search_api to register the shutdown function.
• hook_node_update() runs, here workbench_moderation registers its shutdown function.
• hook_entity_update() runs after that, here search_api would register its shutdown function - but it is already registered.

There could also be other scenarios where the order of shutdown functions would be different, e.g. if another entity gets saved earlier in the request.

I'm unsure whether this really warrants that additional code and complexity.

The same can be achieved in a simpler and more transparent way.

The patch in #6 has a problem, if search_api_index_specific_items_delayed() is called within another shutdown function. In that case, the prepended function is never called.

Instead we need this:

    // Register the shutdown function relative to other shutdown functions from
    // known contrib modules, so that the main code will run after other
    // shutdown functions, especially after workbench_moderation_store().
    // To achieve this, append a shutdown function which appends another
    // shutdown function.
    drupal_register_shutdown_function(
      'drupal_register_shutdown_function',
      '_search_api_index_queued_items');

Here is the patch that fixes the issues what @donquixote mentioned in https://www.drupal.org/project/search_api/issues/2930706#comment-13832461 comment.

Thanks a lot for your work on this. I just updated the comment and code style a bit (making the interdiff pretty useless, I guess …).
Could someone else please confirm that this works for them? Then I can commit.

Could someone please test this?

Hi @drunkenmonkey, I just tested this patch and it works great! Thank-you to everyone for working on this. +1 for RBTC.

Great to hear, thanks for testing and reporting!
Committed. Thanks again, everyone!