docs(update): correct doctor read-only and backend verification guidance

[edrlu]

Problem

docs/update.md says text-mode agent-reach doctor installs or preserves Agent Reach skills and implies every multi-backend channel reports an active backend.

On current main (1221ecd), _cmd_doctor() uses Config(read_only=True) and never calls _install_skill(). Some login-backed channels intentionally return active_backend: null because Doctor avoids implicit credential or browser-session probes.

Proposed fix

• describe Doctor as read-only
• keep skill refresh explicit with agent-reach skill --install
• explain that active_backend is only populated after verification and may safely be null
• add a small documentation regression test

Environment

• macOS
• Python 3.12
• Agent Reach main at 1221ecd