Linux

Open the terminal and copy and paste the commands found in their install guide for Ubuntu:

# Download signing key 
sudo curl -fsSLo /usr/share/keyrings/mullvad-keyring.asc https://repository.mullvad.net/deb/mullvad-keyring.asc

# Add the stable repository
echo "deb [signed-by=/usr/share/keyrings/mullvad-keyring.asc arch=$( dpkg --print-architecture )] https://repository.mullvad.net/deb/stable $(lsb_release -cs) main" | sudo tee /etc/apt/sources.list.d/mullvad.list

# Install 
sudo apt update
sudo apt install mullvad-vpn

More or less: yes.

It's copy and pasting 5 lines into the terminal and hitting enter. It's not that hard. If it's not worth the 15 seconds of 'work' you probably don't need the software that badly.

And it's not the default. Usually you shouldn't add random software sources and download software from some websites. Your Linux package manager should be the source for software. (Software Manager / Store / Synaptics, ... whatever Ubuntu calls it) It installs software with one or two clicks with the mouse, the software there is tested and tied into the rest of the systems and tens of thousands of packages are available. No malware guaranteed, and updates are handled automatically.

And with other Operating systems it's also ridiculous: You need to find the website of some software, avoid malware and copycats that advertise similar software with ads, click download, click 'yes' I accept a download with a harmful extension. Then you need to open the file manager and double click on it. Then a window opens and you need to click 'next'. Accept the terms. Give permission to install and maybe remove a few ticks and choose a location. I'd say it's about the same amount of work and the downside is it doesn't necessarily handle updates and security fixes.

I think Ubuntu doesn't have Mullvad available in their own repository. I took another approach and imported their settings/profile into the VPN/network manager that is available per default on many Linux distributions. No install required at all. But importing the settings isn't easier, so YMMV here. And I think you have to create a profile for each and every country/endpoint which is a bit cumbersome, depending on what you're trying to do with the VPN.

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.