Are there any private email services
protonmail
+1 for mailbox.org
Tutanota and Proton are often recommended services. I personally prefer Tutanota, and their encryption. Though, Proton has a nice suite of services, that is worth looking into. Namely their VPN and Drive…
Tutanota also encrypts email folder and labels names. Last time I checked, Proton does not.
E-mail is not a private service by default. You can “try” to mitigate some privacy flaws using PGP for example but PGP is not widespread to be something useful.