We also get state issued ID card with PKI. We can access tons of services. Last I read I can buy a house, fully remotely. Including notary services via video call + all parties need to sign stuff with our ID card.
We get health results via email as an encrypted pdf, where password is given at the time when I submit samples.
Many business also use ID card to sign contracts between parties.
Bank transactions involve Smart-ID, 2FA app that I have to authorize via ID card for remote setup for any new device. (It involves generating new certificates) Smart-ID is developed by Estonia and is very convenient, secure way to authorize payments.
As of communication, no state issued email. However we usually get email notifications, for example from state tax service, that we should log in and read whatever we have to.