Linux

AFAIK, most distros will also have a package manager/software center where you install flatpaks (or snaps if you are on ubuntu). Think of flatpaks akin to mobile apps where everything needed is all together in one package. Not all apps will be flatpaked though, and VPNs tend to be nearly always direct binaries due to needing some higher level permissions than what flatpaks will allow.

Essentially, what im saying is no, not all apps need to be manually installed, but some might need to for one reason or another. And sometimes, knowing a little about how some of these apps are installed might actually help you understand linux a little more (it has in my case)

If Mullvad is not available as a Snap or Flatpak (2 ways of installing self-sufficient auto-updateable packages without dependencies on other packages) then youre probably stuck with either adding this 3rd party repository (something which isn't always recommendable either) which gives you automatic updates or using a .deb installation file like you would probably prefer and then manually retrieving updates when needed.

Anyways, others have told you as much already anyways. What I'd like to add is that it is definitely worth it to learn to work the terminal. I get that there are many people looking for an alternative to Windows or just an open approach to computing in general without looking for added complexity. Who wants complexity right? Whether such an experience exists in the Linux world is probably subjective. Ubuntu has definitely been a safe bet for the flattest learning curve required since its inception in 2004. But its still a niche thing that won't experience user-friendly support from everyone (ie Mullvad).

So one could conclude that in order to truly be "free" (as in Free Software freedom) one needs to claim that freedom. You will fuck things up. You will learn from your mistakes. You will regroup and you will grow as a user and dare I say PC-curious person.

I know you're on ubuntu, but installing programs depends on your distribution. Some programs are in your software library, some aren't. But there will always be a way to get the program. For instance, I use Gentoo and Mullvad. The way I set it up is with Wireguard so I control it through the terminal, this is because Gentoo has no mullvad app. Otherwise, you can often add new libraries to your system. Again, on Gentoo Steam is not in my repository by default. So, I added the steam repository to my system so I could get it. For Mullvad, I'm pretty sure they offer a deb package, which Ubuntu can use. Otherwise, some other distributions offer a mullvad app in their repository by default. Try other distributions and see what clicks. A lot of linux is experimentation. I personally prefer doing a lot of things fairly manully, so I use Gentoo with essentially only a terminal for control. Linux Mint, Devian, Arch, Void, Nix, Gentoo; there's tons of choices so there's going to be something that you click with.

That is simple. About as simple as it gets. The more complex method involves figuring out what VPN software Mullvad really uses, figuring out your keying material, fighting with NetworkManager...

tl;dr - Follow the directions.