What is required for undercurl support in terminals that support it, e.g. kitty?

printf '\e[4:3mUnderlined\n' works outside of tmux, but not inside.
I've tried wrapping it in the Ptmux wrapping sequence also without success (printf '\ePtmux;\e\e[4:3m\e\\Underlined\n' ).

@bfredl left some insights in neovim/neovim#9052 (comment).