Move DOM event handling out of useEntitySearchInput into its component

[gaidheal1]

Summary

useEntitySearchInput was named and positioned as a logic hook, but it reached into the DOM directly for click-outside dismissal and typed its keydown handler against DOM element interfaces. This splits it along the platform boundary, per #573.

• Stays in the hook (portable): fuzzy search via fuse.js, result derivation, selection state, the debounce, and the semantic intent of keyboard actions — now exposed as onSelectNext, onSelectPrevious, onDismiss, onCommit instead of a DOM-typed handleKeyDown. onCommit returns whether it took action, so the caller knows whether to suppress the key's default behaviour.
• Moved to EntitySearchInput.tsx (web): the document mousedown listener for click-outside dismissal (component now owns rootRef and calls onDismiss()), and translation of raw KeyboardEvents into the hook's semantic actions.
• window.setTimeout / window.clearTimeout → bare setTimeout / clearTimeout.

This branch is stacked on #680 (extracting the beforeunload guard out of useActivityTimer), since both are part of the #569 DOM-decoupling epic and this one was started from that branch.

Acceptance criteria

• No document or window reference remains in useEntitySearchInput.ts
• No DOM-element-typed parameters (HTMLInputElement, KeyboardEvent) in the hook's public surface
• Clicking outside still dismisses the dropdown
• Keyboard behaviour is unchanged: arrow-key selection, Enter to commit, Escape to dismiss
• Debounce timing behaviour is unchanged
• EntitySearchInput.test.tsx still passes

Test plan

• npx tsc --noEmit — no errors
• npx eslint src/components/EntitySearchInput/ — no errors
• npx vitest run — 410/410 pass (pre-existing Playwright browser-launch error is unrelated to this change)

Fixes #573

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