PHP code written for department dropdown added to registration, can be done via url or backend in WordPress admin Users tab. Department stored as user meta data. Stored data can then be used in web pages to distinguish between different departmental user types.Register / subscribe
User Messaging, WordPress has nothing out of the box for this. I could develop something myself but would take a few weeks. There are no free live chat plugins to communicate with WordPress site users that work. The best paid one is $160 a year. See demo video below.Communication
Once approved by an Administrator new departmental users have an additional ‘shop manager’ role added. This gives them access to WooCommerce (linked to Stripe) to manage collection of invoice payments.Make Payments
In conclusion. I believe this is the best lightweight simplest solution to the requirements provided.