Is there no other way on your system to see what the default browser is? On Gnome you can see a few of your default applications in the settings. And what happens if you open an html file for example? Does it open in Zen? If yes then it appears that Zen is set as your default browser, what more is there to check?
Don't AppImages also have a similar requirement just with stuff that is already installed on many popular distros so many people just don't notice it? I think I read somewhere that running AppImages on systems that even slightly differ from the big popular distros is a pain since you still have to ship this stuff with them but it is more cumbersome than with flatpaks.
If you have apps in your dock you can also use "Super + 1-9" to start those apps. For example i have the browser on the first position and the terminal on the second so i switch between them with Super+1 and Super+2. It's also the same on Windows with apps in the task bar by the way. I am fine with it so far but I have thought about switching to a distro with a tiling window manager but the distro I currently use just doesn't support those and I don't want to leave right now.
This is by far not the first time aswell. I've noticed that there are a lot of people that seem to interpret this community as "a place to post your random shit to".
I recently tried out some terminals but in the end it didn't really make all that big of a difference, maybe because I use tmux so I don't need split functionality. For a long time I used Gnome Console because it came with my distro but then I tried Ghostty because some people said it was the best and I also thought I was missing out. However for me it was mostly the same as before and it was cool in a way but for some reason it didn't really click. Now I am using Wezterm because other people said it's the best and what i like is that it comes as a flatpak and it is configured using Lua. But I could just go back to Gnome Console if I had to.
The cops will get him when he makes a hard right at Saratoga