Mark texts ==> show in annotations

Is there a possibility to mark texts so that the marked passages appear automatically in the annotations or in a new file?

Should be possible via AppleScript (or JavaScript). However, it’s only possible to get the currently selected text as plain text, i.e. bold etc. are lost.

If you need bold etc. then the only way would be UI scripting.

Mark texts in what way?

Like this

I only know this way. Does there exist another way?

Highlights appear in the Tools > Annotations inspector.
You could potentially have your annotation file open in another window and drag and drop them from the inspector but you’d have to try it yourself. It includes more information than you may want but it’s an idea.

And no, there is no automatic function built in to do what you’re thinking of.