

The internet is what you get via your ISP. You’re talking about www which is part of the internet but not the internet itself. There are plenty of things to do on the internet that aren’t www e.g. email works over the internet and I’m not talking about something like gmail but the communication between email servers and between your email provider and you when you use imap or pop3.
Mullvad has content and tracking blocking at dns level builtin (enabled in settings). Having it always on you don’t need to use private dns. If you use other profiles then set the private dns to one of mullvads. On my grapheneos install I use google play services only on another profiles then owner and have apps that require it only in those profiles.