Deleting an account via the web doesn't remove it from the app

Expected behavior

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

Actual behavior

Instead, the account is not removed. The user is brought to the login screen, however they are not in fact logged out. Pressing the back button gets them back into the account. It's possible to navigate throughout the app, with no data appearing.

https://user-images.githubusercontent.com/15107387/167609664-8bbda704-b86b-4555-b448-b2ded0108e43.mp4

Steps to reproduce the behavior

1. Create a new account you'd like to delete.
2. Open that account in WordPress.com on a web browser, and delete it.
3. Head back into the app to look around. Note that you are initially on the login screen, which implies you are logged out - but there is a back button available.
4. Navigate around your account after tapping the back button.

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

Related: deleting a site from the web has similar effects: https://github.com/wordpress-mobile/WordPress-Android/issues/16511

No source files or tests are named. Start by reproducing the account-deletion flow using the listed Android version and app version, then compare the login-screen state with what happens after pressing Back; done means a web-deleted account cannot be re-entered or navigated in the app.