Toolbox search - Connect to external API for large template libraries

[JaneSjs]

• T27584 - type to search
• How to always show the search box in SurveyJS Toolbox and override search to call backend API #7245
• Toolbox - Add search option for toolbox items (suppose if the elements in toolbox is more than 100 and need to search how do we acheive) #2231

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Implement an API so toolbox search can query an external backend and show matching templates (for catalogs with 100+ items).

Usage scenario
A company has 500+ approved question templates in a backend. The Creator shows a small default toolbox.
The user types nps in the toolbox search → the app calls the API → matching templates appear under Templates → the user drags NPS Question onto the survey. When the user clears the search, API templates disappear and the standard toolbox is shown again.

Requirements:

• Add a public toolbox API with a search(query): Promise<IQuestionToolboxItem[]> callback.
• Integrate it into the built-in toolbox search UI (debounce, min query length, ignore/cancel stale requests).
• Register API results as dynamic toolbox items in a dedicated category (localizable, e.g. toolboxCategories.templates).
• Do not require the full catalog in memory — only matched items from the server are added per query.
• When external search is enabled, allow the search box to stay visible regardless of toolbox item count.
• Support hybrid mode: keep filtering built-in items locally while merging API results.
• Default on clear search: remove dynamic API items and restore the standard toolbox.
• Default on new query: replace previous API results (no accumulation).
• Fix internal toolbox/search lifecycle so addItem / filtering does not drop hidden built-in items from actions.