Move 21 search/pagination/scroll/blacklist methods and 8 state
attributes (_current_page, _current_tags, _current_rating, _min_score,
_loading, _search, _last_scroll_page, _infinite_scroll) into
gui/search_controller.py.
Extract pure functions for Phase 2 tests: build_search_tags,
filter_posts, should_backfill. Replace inline _filter closures with
calls to the module-level filter_posts function.
Rewire 11 signal connections and update _on_site_changed,
_on_rating_changed, _navigate_preview, _apply_settings to use the
controller. main_window.py: 3068 -> 2525 lines.
behavior change: none
