Claude experiment (#34577)

Release Notes:

- N/A

---------

Co-authored-by: Conrad Irwin <conrad.irwin@gmail.com>
Co-authored-by: Anthony Eid <hello@anthonyeid.me>
Co-authored-by: Ben Brandt <benjamin.j.brandt@gmail.com>
Co-authored-by: Nathan Sobo <nathan@zed.dev>
Co-authored-by: Oleksiy Syvokon <oleksiy.syvokon@gmail.com>

crates/icons/src/icons.rs

@@ -11,6 +11,7 @@ pub enum IconName {
     Ai,
     AiAnthropic,
     AiBedrock,
+    AiClaude,
     AiDeepSeek,
     AiEdit,
     AiGemini,