Web browsers are generally built with security in mind. Terminal emulators surely much less so. The OpenSSH client probably sits somewhat in between, generally developed with security in mind, but not necessarily consistently expecting malicious servers.
At least for the more prominent terminal emulators i expect they probably devote a great deal of attention to security. They are developing the most commonly used interfaces for linking the most numerous, varied, and/or critical systems on the planet.
Went to the kitty website. No mentions of security.
Went to Alacritty. No mentions of security.
Went to Ghostty. No mentions of security, except for "secure keyboard entry".
None have a "security policy" on GitHub.
All written in memory unsafe languages (C, Zig).