Trust in a job is important. My own work sets 2 or sometimes even 3 reminders for policy changes that can cause a risk. And changes are publically available a month in advance.
Heck, I know since August that we will have less time off next year.

Forgetting the new name of our division is an happy mistake. Changing sick leave procedure is important and requires to be SURE the employee knew about it.
Also email is NOT a guaranteed medium if done online, my dad's email about his train accident was received by my grandma... one year later.

Your managers have absolutely no idea how to manage or communicate with their employees and happily throw them under the bus when the issue comes up. It's not a safe work relationship, stay safe. :(

> it's the employee job to be responsible and to read the email

And it is the manager's job to ensure the employee did his job. If the manager had done their job, they wouldn't have gotten understaffed. An issue was bound to happen with their system. I'm even surprised it wasn't done on purpose tbh.