Actually, at least for this system, it is more like a common API enforced by e-Devlet with a client on e-Devlet, rather than the government tracking your subscriptions. Every time you open the page for this central cancellation system, it queries the providers' servers using a token generated from your digital key (so you can't query random people's info) and shows you if you have a subscription with them or not. If you want to cancel, it basically generates and sends a digitally signed and pre-filled form over digital mail (kind of like e-mail, but legally binding, timestamped, encrypted and mandatory for all corporate entities - like some sort of online notary).

At this point, everything continues as if this system wasn't involved, but now you have proof of intent to cancel. If they don't act on it in 2 work days you are in no obligation to pay for them anymore. And even if you accidentally do pay, you will be refunded.