## What changed
- Detect Rex from `TERM_PROGRAM=rex` or `TERM=xterm-rex` and report its name in terminal diagnostics.
- Enable Kitty graphics for pets in Rex.
- Use the detected terminal identity for Rex's label-only web links, extending that behavior to detection through `TERM`.
## Testing
Add Rex detection coverage for both environment variables and include Rex in the web-link rendering and Kitty graphics support tests.
GitOrigin-RevId: b237e8a6b3af50a55080573dc1e0badc2c139b42