Cache data on available config updates

What do you propose we actually cache?

In ConfigSyncLister, we could cache:

Configuration Comparisons:
Precomputed differences between active and target configurations (e.g., added, updated, deleted items).

Changelists:
Detailed lists of configuration changes, including metadata like labels, types, and dependencies.

Extension Lists:
Precomputed lists of extensions with configuration to synchronize.

These items are computationally expensive but can be invalidated and recomputed as needed when the underlying data or context changes.

I am not sure if we will be able to detect changes in order to invalidate the cache once we have it, but I could be missing something.

I like the idea of caching the config comparisons and changelists.

I think we might just need to add a "refresh" button to the config distro form so make manual cache invalidation possible.

Do you think a custom cache bin is in order to do all of this, or do you recommend a specific cache bin? https://api.drupal.org/api/drupal/core%21core.api.php/group/cache/11.x

The main concern I have about invalidating the cache is during automated processes, like site updates for example, how do we ensure the module continues to function the same way (not needing a cache rebuild before drush cd-update) and also cache the comparisons and lists.