New Linux user here. Is this really how I'm supposed to install apps on Linux?

Asking why something is the way it is makes you more of a “Linux user” than many.

You make a valid criticism; there’s definitely a learning curve to installing software if you choose to do it that way (since it’s not similar to other OSs), and it’s not automatically explained to new users by using the OS.

Here’s the understanding of it I’ve come to, if you’re interested:

Like others have said, the .deb file would be the equivalent of an .exe file on Windows. Like many .exe files, unless they include an auto-updater, they won’t automatically update.

A key difference I would like to point out is that Linux package managers often update and manage parts of the OS in addition to extra software. Windows and macOS both update their OS separately.

“Ubuntu Software Center” is similar to the “Microsoft Store” on Windows and the “App Store” on macOS. Like those, it’s user friendly and provides automatic updates, but it also doesn’t have every app. You can ensure those apps are safe because the company behind the OS verifies them.

“apt-get” is the default package manager for Ubuntu. That is the tool doing the heavy lifting underneath, and what those commands Mullvad gave are for.

Mullvad could have provided a script to download and run that executes those commands for you, but then you wouldn’t know what it’s doing, especially with it needing admin permission. With how security-oriented Mullvad’s brand is, I think that’s one potential reason they explain the steps and have the user do it instead.