When I try to ssh into one of my servers using this terminal I get the following:

  missing or unsuitable terminal: xterm-ghostty
  Connection to xxx.xxx.xxx.xxx closed.

(IP address removed by me.)

It turned out that this is associated with how I automatically run tmux by having the following kind of config for how I connect to that server.

  Host server3000
   IdentityFile ~/.ssh/host_specific/foo/bar/server3000/id_ed25519_baz
   RequestTTY yes
   RemoteCommand /usr/bin/env tmux new-session -A -s '%L'

Whereas if I outcomment the RemoteCommand setting in my ~/.ssh/config of the laptop I'm connecting form, I can connect fine even using Ghostty as my terminal and from

  env | grep ^TERM=

I get output

  TERM=xterm-256color

in the initial normal shell.

And if I run tmux, then inside of it from

  env | grep ^TERM=

I get output

  TERM=tmux-256color

So there seems to be some termcap stuff I'd have to figure out if I want to use Ghostty and still be able to run tmux automatically in the way I'm currently doing without problem when using the Terminal that ships with macOS and ssh'ing into my servers.