fix(search): wait for committed IME input before searching

[ouchihao]

The search input forwards raw input events while an IME composition is still in progress, updating filters and searching for unfinished text. Bind through a writable computed value with native v-model so Vue handles composition, while keeping the existing update and debounced search events.

Validation:

• Covers composition commit, immediate plain-text updates with debounced searches, and external model updates. 1 regression cases fail before the fix; all 3 focused cases pass after it.
• Focused tests plus the 17 Makefile critical suites: 230 tests passed.
• vue-tsc --noEmit, full frontend ESLint and git diff --check passed.

Tests use mocked APIs; no live-server validation.