fix(search): full-text indexes+caching

Adds a few new indexes to handle full-text searches instead of doing
`ILIKE` matching, improving performance substantially.
Alongside that, a few other things were done in order to improve search
performance, such as caching filter values so they're not computed on
each request to /api/roms. Overall, this should have a very noticeable
impact on large collections when using the search feature.

backend/tests/handler/test_db_handler.py

@@ -219,6 +219,55 @@ def test_filter_by_search_term_with_multiple_terms(platform: Platform):
     assert actual_rom_ids_single == expected_rom_ids_single
 
 
+def test_filter_by_search_term_multi_word_and_ranking(platform: Platform):
+    def _add(name: str) -> Rom:
+        fs = name.replace(" ", "_")
+        return db_rom_handler.add_rom(
+            Rom(
+                platform_id=platform.id,
+                name=name,
+                slug=name.lower().replace(" ", "-"),
+                fs_name=f"{fs}.zip",
+                fs_name_no_tags=fs,
+                fs_name_no_ext=fs,
+                fs_extension="zip",
+                fs_path=f"{platform.slug}/roms",
+            )
+        )
+
+    ff = _add("Final Fantasy")
+    ff7 = _add("Final Fantasy VII")
+    fantasy_final = _add("Fantasy Final")  # both words, reversed order
+    _add("Final Combat")  # only "final"
+    _add("Angelique - Voice Fantasy")  # only "fantasy"
+    _add("Super Mario World")  # neither word
+
+    results = db_rom_handler.get_roms_scalar(search_term="final fantasy")
+    result_ids = [r.id for r in results]
+
+    # Only titles containing BOTH words appear (AND semantics).
+    assert set(result_ids) == {ff.id, ff7.id, fantasy_final.id}
+
+    # Exact-order phrase matches rank above the reversed-order match.
+    assert result_ids.index(ff.id) < result_ids.index(fantasy_final.id)
+    assert result_ids.index(ff7.id) < result_ids.index(fantasy_final.id)
+
+    # The relevance ORDER BY must also survive the group_by_meta_id subquery
+    # wrapping used by the gallery (each ROM here is its own group).
+    grouped = db_rom_handler.get_roms_scalar(
+        search_term="final fantasy", group_by_meta_id=True
+    )
+    assert {r.id for r in grouped} == {ff.id, ff7.id, fantasy_final.id}
+
+    # An explicit sort takes priority over relevance: ordering by name asc puts
+    # "Fantasy Final" first (relevance is only the tiebreaker here).
+    explicit = db_rom_handler.get_roms_scalar(
+        search_term="final fantasy", order_by="name", order_dir="asc"
+    )
+    explicit_ids = [r.id for r in explicit]
+    assert explicit_ids.index(fantasy_final.id) < explicit_ids.index(ff.id)
+
+
 def test_sibling_roms_empty_fs_name_no_tags_not_matched(platform: Platform):
     """ROMs with empty fs_name_no_tags should NOT be matched as siblings.