If you use a laptop as a second screen via a program, does Windows recognize this laptop as an additional screen?
It depends on which program you are using.
It's very easy to do.
You can also find tons of tutorials on YouTube if you don't know how to do it
Which one would you recommend?
None at all, but the standard Windows tools: Miracast.
https://www.wintotal.de/tipp/laptop-als-monitor-nutzen/