P3.4: cuekit doctor zellij probe (multiplexer Phase 3)

[takemo101]

Phase 3, issue P3.4 — part of the multiplexer backend abstraction implementation plan.

Design: docs/designs/cuekit-multiplexer-backend-design.md

Prerequisites: P3.3 merged.

Outcome

cuekit doctor runs the zellij version probe when zellij is the configured (or fallback-detected) backend, and reports a per-backend status line.

Files

• Modify: packages/cli/src/doctor.ts

Steps

• Add a zellij probe (binary present, version ≥ baseline pinned by P3.0 spike).
• Surface "active backend" + "fallback applied?" in output.

Acceptance

Doctor output covers tmux, zellij, and fallback states.