[Bug] Auto-Focus Search Input upon Navigating to Global Search Route

Module: src/app/features/search/

Description
Navigating to `/search?q=query` from the top header search bar loads the Search page, but focus is not automatically retained on the input field.

Steps to Reproduce
1. Click the top header search bar.
2. Type a query and hit Enter.
3. Page routes to `/search`, but the user has to click the search input field again to modify the query.

Expected Behavior
The search input on `/search` should automatically focus on page load (`autofocus` or `viewChild` focus call).

Proposed Implementation
- Add `(afterViewInit)` or `Effect` in `SearchComponent` to call `.setFocus()` on the Ionic input component.

Start in src/app/features/search/ and inspect SearchComponent together with the Ionic search input. Reproduce navigation from the top header search bar to /search?q=query, then check the component lifecycle or effect used for focusing. Done means the search input is focused after the route loads and the query can be edited immediately.

Written by the indexing model from the issue text.