Deleting a site via the web doesn't remove it from the app

Expected behavior

I expected that after I deleted a site from the web, it would be removed from the app immediately.

Actual behavior

Instead, the site is not removed. My Site Menu is still displayed with the site address and title. All items can be tapped, and show various errors. For instance:

Stats: "Data not loaded" grey toast message
Media: "Media couldn't be refreshed at this time"
Posts: "You don't have permission to view or edit posts"
Site Settings: Site Settings appears and you can scroll through them a bit, but then are directed back to My Site Menu and shown "Couldn't retrieve site info" blue toast message.

Steps to reproduce the behavior

1. Create a new site you'd like to delete. I did this on an account with no existing sites.
2. Open that site in WordPress.com on a web browser, and delete it.
3. Head back into the app to look around, and notice that you still have that site selected and can navigate around the app with that site.

Tested on Samsung Galaxy S21, Android 12, WPAndroid 19.8-rc-2.

Reproduce the flow by deleting a site on WordPress.com, then returning to the Android app and opening My Site Menu. Trace how the app refreshes or invalidates the selected site after deletion, and confirm that the deleted site and its menu are removed without the reported data, permission, or site-info errors.