* http://jdebp.uk./Softwares/nosh/guide/commands/TERM.xml#MIS-...
* https://invisible-island.net/xterm/xterm.faq.html#other_vers...
The correct terminal type, per Dickey terminfo, is "kitty". (The PuTTY variant KiTTY is apparently also "putty".) And the terminfo database lends itself both to copying individual records and to having extra records in one's home directory.
* https://invisible-island.net/ncurses/terminfo.ti.html#tic-ki...
* https://invisible-island.net/ncurses/terminfo.ti.html#tic-pu...
ncurses from FreeBSD Ports is built with terminfo, but the ncurses from base uses termcap. Kind of a mess :)
Most application ports have USES=ncurses without arguments, which means they will prefer the ports ncurses — if it's installed at build time. Official binary packages are built without it installed of course. So rebuilding the ncurses apps you care about would make them use terminfo.
Also you can convert terminfo to termcap: https://invisible-island.net/ncurses/man/infotocap.1m.html