Pods Alternative Cache does not flush the rewrites, however Pods does flush rewrites when you create, update, or delete a pod. This is meant to handle cases where you’ve changed something that affects the rewrites. It normally causes no issues during that process though.
When you Clear Pods Cache, we flush the permalinks then too, so it probably gave a kick to the rewrite issue you were having — it wasn’t something cached on our end that had to be cleared.
I should note that my original suggestion to use Pods Alt Cache wasn’t based on the 404 error you reported, just that I thought it might possibly be related to the object cache or some other similar issue.
I’ve seen 404 issues happen on WP updates usually on projects of mine, which is odd. This happens when a plugin tries to flush rewrites too early — something our plugin has been very careful to ensure happens after the init action (we run our flush operation in the wp_loaded action which is the very next action after the init action).
The init action is the accepted standard action where post types, taxonomies, and rewrites are registered. Your best bet may now be to investigate some of your other plugins to see if you find a call to code that might look similar to this $wp_rewrites call:
https://github.com/pods-framework/pods/blob/bd5129003a313b899693cda4757e35c47b52569c/classes/PodsInit.php#L873