This merely sort files by their creation data or last date modified. It has nothing to do with when the font was activated.

I found a way to do this in Windows: open a command prompt, go to the directory C:\WINDOWS\FONTS and do a DIR /O:D (directory, order by date).

I don't get what could be so hard - each file has its own creation date, so OS can easily check which font is new and which one is older. And even if it made type menu slower - I'd still have it. I could turn it on when I need a font that I know I installed recently, but have forgotten its name, and - having found it - turn it off again.

This is probably not possible. The OS (Windows or Mac) likely doesn't record this or report it to applications. The closest you could get is to have InDesign constantly monitor the Font menu and log changes so that newly installed or activated fonts can be shuffled to the top. That doesn’t sound too difficult, but it could slow performance as the log gets longer and longer as more fonts are activated and deactivated. As the log gets longer the time needed to search through it and sort by activation date and time would make just opening the font menu a nightmare. If you have to wait two seconds every time you open the font menu you will either stop opening the font menu or turn the sort feature off and flush the log.

And I mean it in drop-down font menu of course.