perf(search): a one- or two-letter last word is matched whole, not as a prefix

A 1-2 letter prefix matched most of the library and ts_rank scored every
match: "m" took ~4-8 s on prod against ~150 ms now. The prefix match
starts at three characters (MIN_PREFIX_LEN); shared by the YouTube feed
and the Plex library search.

backend/tests/test_utils.py

@@ -1,8 +1,8 @@
-"""iso(): the single date/datetime→JSON serializer the routes share (R6 S1a)."""
+"""iso(): the single date/datetime→JSON serializer the routes share (R6 S1a); to_tsquery_str()."""
 
 from datetime import date, datetime, timezone
 
-from app.utils import iso, normalize_description
+from app.utils import iso, normalize_description, to_tsquery_str
 
 
 def test_none_maps_to_none():
@@ -56,3 +56,19 @@ def test_normalize_description_single_line_unchanged():
 def test_normalize_description_folds_crlf_line_endings():
     # splitlines() folds CR/CRLF to \n — a documented, benign line-ending normalization.
     assert normalize_description("a\r\nb\r\n\r\nc") == "a\nb\nc"
+
+
+def test_tsquery_prefix_matches_a_last_word_of_three_or_more():
+    assert to_tsquery_str("ti amo magyar") == "ti & amo & magyar:*"
+    assert to_tsquery_str("min") == "min:*"
+
+
+def test_tsquery_matches_a_short_last_word_whole():
+    # A 1-2 letter prefix made ts_rank score most of the library (5-8 s on prod, E31 S4e).
+    assert to_tsquery_str("m") == "m"
+    assert to_tsquery_str("minecraft 4k") == "minecraft & 4k"
+    assert to_tsquery_str("ti amo m") == "ti & amo & m"
+
+
+def test_tsquery_without_a_word_is_none():
+    assert to_tsquery_str("?! --") is None