Covers #430's full scope so far: the picker itself, the model-selection
dialog, periodic re-discovery, and the session-busy/toast/CLAUDE_CONFIG_DIR/
context-length/llama-swap-conflict fixes found through live validation
against a real llama-swap server.
Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01RqZeHrRS6DYcGcGX2p9EwG
