Interactive model selector: arrow key navigation stuck and no mouse support

## Description

The `/models` interactive selector has usability issues:

1. **Arrow key navigation appears stuck** — the highlight shows on one model but pressing up/down arrows does not move the selection. This occurs across multiple Node.js versions (19, 22, 24) and Copilot CLI versions (1.0.60, 1.0.61).

2. **No mouse support** — users cannot click to select a model from the list. Adding mouse click support for the interactive model picker would greatly improve usability.

## Environment
- OS: Linux (RHEL/CentOS, NFS-mounted home)
- Terminal: X11 terminal (xterm)
- Shell: tcsh
- Node.js: tested with v19, v22.14.0, v24.16.0
- Copilot CLI: tested with 1.0.60 and 1.0.61
- TERM: xterm / xterm-256color (same behavior with both)

## Workaround
Using `/model ` directly instead of the interactive picker.

## Expected Behavior
- Arrow keys should move the highlight between models
- Ideally, mouse click should also be supported for selection

Start at the `/models` interactive selector and reproduce the issue with arrow keys in the reported terminal environment. Done means the highlight moves between models with up/down arrows and a mouse click selects a model.

Written by the indexing model from the issue text.