Sorry for the confusion!
Yes, you are right, dragging the calibre window to the TV on the extended desktop seems the simplest and best option, at least regarding the part of the "viewing" what's in the library.
What's a bit more cumbersome is the part of the "controlling" what you see by a physical keyboard and mouse when sitting comfortably on a couch.
BTW, how do you control the virtual on-screen keyboard, if needed, by the mouse?
I've also tried the android app
unified remote to control the PC giving you different virtual remotes like mouse, keyboard, slideshow and others, it works pretty well with calibre as well.
What also were helpful would be the possibility to quickly switch the user interface of calibre to a sort of saved "
presenting view mode" more suitable for the purpose of simply
showing the content to others on a distant screen: e.g. bigger fonts, menu with its icons deaktivated ... Would you have a hint for that?