bug(live): node filter accepts input before its handler is ready #2094

The Live node-filter input accepts text before its input handler is installed. Text typed while the initial node request is pending is never processed after loading finishes.

Reproduced on unchanged 9eb3098 in Chromium with the real fixture API, holding /api/nodes until after typing te:

{"before":{"bound":false,"value":"te"},"after":{"searches":0,"expanded":"false"},"afterAnotherKeystroke":{"searches":1,"suggestions":10}}

The instrumentation only recorded listener attachment and delayed the real request; it did not replace API data or the handler. After the handler attaches, the existing text produces no search. One further keystroke produces suggestions normally.

public/live.js renders #liveNodeFilterInput, awaits loadNodes(), then attaches the input listener. This also explains intermittent failures of the core #1110 browser checks: they wait for a visible input, then type before it is ready.

Expected: either install the handler before awaiting node loading, or keep the input disabled until it is wired. Preserve any already-entered input if it remains editable during loading. Add a browser regression with delayed initial loading; do not solve this with a fixed sleep or a longer test timeout.

Found while validating #2091; its packet URL changes do not touch this behavior.