Thank you for the feedback.
I actually have thought about (and already implemented) e-mail types and worker qualifications so if you give a technical e-mail to the marketing department it will take longer to complete. For this playable demo I have given every worker the same qualifications (all e-mail types except spam).
The e-mail with multiple people is an interesting idea that I have put on my post-jam To-do list.
Post-jam I'll also probably introduce limited e-mail spawning space. This should solve e-mail spawning and simultaneously provide an incentive to get rid of spam mail.
The main system for the progress bar is also already kind of there, I simply have to learn how animations work in Unity and then I'll have to code that the progress bar fills according to the elapsed time.