[firewalker06]

Summary

• prioritize agents with awaiting_input or an active latest_inquiry at the top of Quick Agents and the shared Relevancy sort
• preserve the existing no-action demotion, activity recency, and deterministic name tie-breakers for every other agent
• add focused comparator coverage and an isolated Chrome smoke mode with mobile and desktop captures

Verification

• bundle exec ruby test/remote_ui_agent_search_test.rb
• bundle exec ruby test/remote_server_test.rb
• bin/test
• TYCHO_REMOTE_UI_QUICK_AGENTS_PRIORITY_ONLY=1 TYCHO_REMOTE_UI_CAPTURE_DIR=/tmp/tycho-fizzy-235-evidence.mEOiFo bin/remote-ui-smoke

Implements Fizzy #235. The card remains open for independent review.