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

Matrix is more like discord, no phone numbers, just email, and you can make big groups with different channels within. More meant for communities then something like Signal, that's mostly for 1:1 conversation or small groups

What advantage would it give me over other services? Keeping the discord example i said above, no tracking, possibility to have end to end encryption, and open source code, along with the ability of having different instances that can communicate to each other, just like here on lemmy, so if you don't trust anyone else you can run your own instance

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

It's mostly good already, but as with many other privacy focused services it lacks a wide adoption, so most of the communities there are about privacy, Linux and that type of stuff.

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

The most used client, Element, is IMO very easy to use, you can directly register through there, and you get the choice of choosing between the official matrix.org instance (which on certain occasions is laggy due to the many people using it), or other instances