As the title says. This is similar to this answered question, but before marking it as a duplicate please note there's a problem with that post: it is outdated.
Basically, all existing answers that I found on various sites refer to pressing some
Animate button as a way of triggering the process of saving to a file, and the button has disappeared. On the current interface the most similar one I found is
Render → Render Animation at the top menu, but all it does is creating a new window with a playback, which has no obvious way of finally triggering the save to a file (and I also found a
Sequence Render Animation menu elsewhere, which seems to do the same thing).
I've been searching for about two hours already, and I'm kind of becoming desperate at this point. I find amusing that Blender even has a documentation about setting up a video output, but it lacks the most crucial step: how to make those properties result in an actual video file.
For reference, below is a screenshot of the current interface.
At the top-right half of the window you can see a panel with video output settings: a codec, a quality, and most importantly there's an output directory. But whatever I do in the program, the output directory is always empty.