fix: make documentation search usable

[smiggleworth]

Fixes #8.

The docs search trigger now focuses the input when opened by click as well as keyboard shortcut. Search requests are generation-guarded so stale lazy-index loads cannot overwrite newer input, and failures leave a visible retryable state instead of a permanent loading state.

Validation:

• npm run fmt -- --write src/pages/docs/search.tsx
• npm run typecheck
• npm run test:unit
• npm run check

[Copilot]

Pull request overview

Improves the documentation search dialog interaction so it reliably opens/focuses, handles lazy index loading without stale updates, and surfaces a visible failure state instead of getting stuck loading.

Changes:

• Centralizes “open search” behavior to focus the input for both keyboard shortcuts and trigger clicks.
• Adds a generation/cancellation guard around the async lazy import to prevent stale searches from overwriting newer input.
• Introduces an error state UI when loading/search fails.

Comments suppressed due to low confidence (2)

src/pages/docs/search.tsx:35

• After persisting searchGeneration in state, runSearch still uses ++searchGeneration and compares against searchGeneration as if it were a mutable number. Update the increment/check logic to use the getter/setter (searchGeneration() / setSearchGeneration(...)) so stale async searches cannot clobber newer ones.

  const runSearch = async (value: string) => {
    const generation = ++searchGeneration;
    setQuery(value);
    setError(false);
    if (!value.trim()) {

src/pages/docs/search.tsx:56

• close() currently mutates searchGeneration directly. Once searchGeneration is stored in component state, increment it via the setter so any in-flight searches see the updated generation and abort correctly.

  const close = () => {
    searchGeneration += 1;
    setOpen(false);

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