There is no 16bit. You cannot alter the 24bit (at least not on your average terminal emulator).
Same is true for 8bit. Most terminal emulators tend not to support altering those colours either.
In practice, the only application I use that I've had to configure the colours for was tmux. But I tend to forget about tmux because its one of those applications that needs a lot of a configuration from the outset anyway (in my opinion at least).
There might be other "must have" tools that set the background colours too. I've either not needed them personally, or have completely forgotten about them
Same is true for 8bit. Most terminal emulators tend not to support altering those colours either.
In practice, the only application I use that I've had to configure the colours for was tmux. But I tend to forget about tmux because its one of those applications that needs a lot of a configuration from the outset anyway (in my opinion at least).
There might be other "must have" tools that set the background colours too. I've either not needed them personally, or have completely forgotten about them