The mention of "Unofficial" is due to the package format. It's a rather long and boring tale, but essentially there are several formats a piece of software can be distributed as. As with most things in life, there are pros & cons but I don't think it's worth getting into that right now.
What's happening here is that the developers of SimpleScreenRecorder did not package their project using the Snap package format. What you are seeing is the work of the community in action, hence the "unofficial" label in the package name.
However, you should be able to find another match for SimpleScreenRecorder if you search in the Software store, one that comes from "Zorin OS" (this will install the native Debian package instead). I'm not on Zorin OS right now and I can't check for myself, but give it a try. Otherwise, you can run this command in a terminal window (you will find "Terminal" in the applications menu):
sudo apt install simplescreenrecorder
And that will install it as well.
One of the unfortunate downsides of alternative package formats, such as Snaps or Flatpaks, is that they require an additional runtime which is a bundle of all the necessary libraries to run instead of the ones installed in your OS. This means that it'll take longer to download if it's the first time you install any Snap package, or if a newer runtime is needed.
It can be very frustrating, which is why I'd suggest leaving Snaps and Flatpaks as the last resource, and default to use the native Debian package format whenever possible; you might see it referred to as APT or Zorin OS in the Software store.
Additionally your screenshots show a downward triangle to the right of 'snap'. Click on the down arrow to see if there is an Apt option, it will be labelled Zorin (APT).
