It’s rude to install a terminfo on a remote machine (which you may not be the owner of). It’s a preposterous for a terminal emulator to install things on a remote machine just to make it work.
Host * SetEnv TERM=xterm-256color
Host *
SetEnv TERM=xterm-256color
SendEnv COLORTERM TERM_PROGRAM TERM_PROGRAM_VERSIONOtherwise, there is no need to install anything, you should just set the environment variable TERM in the remote computer to one of the xterm variants and then modern terminal emulators like kitty or ghostty will still work fine, but of course only as long as you use the xterm-compatible subset of their features.