What would be the utility for someone, who cares about privacy and currently uses Signal and email for communication?

Your organization can't host a federated Signal server, and email isn't private.

Is Matrix anything good already, or is it something with potential that's still fully in development?

My previous organization has used it for over 4 years without issues, however mostly limited to text.

How tech savvy does one need to be to use Matrix?

Simply using? Not very much, basically like Lemmy.