fix: ListenBrainz similarity is stored relative to the seed's best, and the candidate arms keep tier order (#6177)

LB's similarity scores are counts (16 to 1445 for recordings, to 10,875
for artists), and they reached a scorer that reads similarity as 0 to 1.
One edge added 64 to 5,800 points under Songs-like, so likes, skips and
recency stopped mattering for any candidate with an edge.

- ResolveListenBrainzTrackEdges divides each edge by the seed's best
  score in its whole cached answer. The cache keeps the raw answer.
- The worker stores matched and unmatched artist rows over the seed's
  top artist.
- Migration 0096 rescales the rows already stored.
- The candidate arms hold sim_score bands so tier 1 stays above tier 2:
  lb_similar 0.5 + 0.5 x edge, tag_overlap halved, likes_overlap 0.3.
  Otherwise a seed's weaker LB edges fell below a shared genre tag.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

internal/db/queries/recommendation.sql

@@ -62,6 +62,18 @@ WHERE t.id <> $2
 -- the determinism they promise; radio passes a fresh value per request and
 -- keeps varying, which is what a radio should do.
 -- Returns same shape as LoadRadioCandidates plus similarity_score column.
+--
+-- sim_score BANDS keep the tiers in order (rule 131, #6177). Similarity edges
+-- are stored relative to the seed's best match, 0 to 1, so the arms are placed
+-- in bands rather than compared raw:
+--   tier 1  lb_similar                      0.5 + 0.5 × edge   (0.5, 1.0]
+--   tier 2  similar_artists, coplay_artists 0.5 × edge         [0, 0.5]
+--           tag_overlap                     0.5 × share of the seed's tags
+--           likes_overlap                   0.3, flat
+--   tier 3  taste_overlap, random_fill      0
+-- Without the bands, the seed's weaker LB edges fell below a shared genre tag
+-- and the flat likes score, and the one arm that measures the seed lost to
+-- the ones that guess.
 
 WITH
 seed_artist AS (
@@ -87,7 +99,7 @@ excluded_ids AS (
     WHERE q.user_id = $1
 ),
 lb_similar AS (
-    SELECT ts.track_b_id AS track_id, ts.score AS sim_score
+    SELECT ts.track_b_id AS track_id, 0.5 + 0.5 * ts.score AS sim_score
     FROM track_similarity ts
     WHERE ts.track_a_id = $2
       AND ts.source = 'listenbrainz'
@@ -117,8 +129,8 @@ similar_artists AS (
 ),
 tag_overlap AS (
     SELECT t.id AS track_id,
-           (count(DISTINCT trim(g))::float8
-            / GREATEST((SELECT count(*) FROM seed_tags), 1)) AS sim_score
+           0.5 * (count(DISTINCT trim(g))::float8
+                  / GREATEST((SELECT count(*) FROM seed_tags), 1)) AS sim_score
     FROM tracks t
     LEFT JOIN LATERAL regexp_split_to_table(coalesce(t.genre, ''), '[;,]') AS g_split(g) ON true
     WHERE trim(g_split.g) IN (SELECT tag FROM seed_tags)
@@ -130,7 +142,7 @@ tag_overlap AS (
     LIMIT $7
 ),
 likes_overlap AS (
-    SELECT gl.track_id, 0.6::float8 AS sim_score
+    SELECT gl.track_id, 0.3::float8 AS sim_score
     FROM general_likes gl
     WHERE gl.user_id = $1
       AND gl.track_id NOT IN (SELECT id FROM excluded_ids)