fix(search): surface exact short profile names (#5480)

## Summary

- prioritize exact whole-lexeme matches within short kind-0 prefix
searches
- preserve the existing prefix result set, pagination, community/channel
scope, hydration, and authorization path
- add a Postgres regression where newer noisy `jm…` profiles saturate
the bounded page

## Why

Desktop mention autocomplete starts searching after one character. The
`jm` profile is indexed and matches both `jm:*` prefix search and
standard full-text search, but production prefix search returns a full
50-result page without it. Raw profile JSON supplies enough unrelated
`jm…` lexemes that newer equal-rank matches fill the bounded page before
the exact short display name.

Changing clients would leave deployed Desktop 0.5.8 installations
broken. This shared search-layer compatibility fix changes ordering only
for `Prefix + kinds:[0] + query length <= 2`; message search, longer
profile typeahead, and agent eligibility are untouched.

## Validation

At commit `ff88761135d5045139aeb3da14d08cbfba203169` with a clean
worktree:

- `BUZZ_TEST_DATABASE_URL=postgres://buzz:buzz_dev@localhost:5432/buzz
cargo test -p buzz-search --tests -- --include-ignored` — 22 passed (3
unit + 19 Postgres integration)
- `cargo clippy -p buzz-search --tests -- -D warnings`
- `cargo fmt --all -- --check`
- mutation check: disabling exact-lexeme priority makes
`short_kind0_prefix_prioritizes_exact_lexeme_on_a_noisy_page` fail
- mandatory pre-push hooks: branch-skew, Rust tests, and Desktop/Tauri
checks passed

## Risk

Low. The extra ordering predicate applies only to one- or two-character
prefix searches restricted exactly to kind 0. It does not add
candidates, bypass filters, or alter access control. Exact matches move
ahead of broader prefix matches; all remaining ordering stays relevance,
recency, then event ID.

Signed-off-by: Wes <wesbillman@users.noreply.github.com>
Co-authored-by: Carl <c7ebe626f000404285d3686e1dc74cc07cc60a9754a150041ba132e14bd3e2ec@buzz.block.builderlab.xyz>

crates/buzz-search/src/query.rs

@@ -229,6 +229,14 @@ pub async fn search(pool: &PgPool, query: &SearchQuery) -> Result<SearchResult,
     };
     let page = query.page.clamp(1, PAGE_MAX);
     let offset = ((page - 1) as i64) * (per_page_actual as i64);
+    // Profile typeahead uses broad prefix matching. For one- and two-character
+    // queries, a busy community can have enough newer prefix matches to push a
+    // short exact display name off the bounded first page. Keep the same result
+    // set and pagination contract, but put rows containing the whole lexeme
+    // first for this one narrow caller shape.
+    let prioritize_exact_profile_lexeme = query.mode == SearchMode::Prefix
+        && query.kinds.as_deref() == Some(&[0][..])
+        && search_text.chars().count() <= 2;
 
     let mut qb: QueryBuilder<sqlx::Postgres> = QueryBuilder::new(
         "SELECT id, kind, pubkey, channel_id, \
@@ -292,7 +300,13 @@ pub async fn search(pool: &PgPool, query: &SearchQuery) -> Result<SearchResult,
         qb.push(")");
     }
 
-    qb.push(" ORDER BY rank DESC, created_at DESC, id LIMIT ");
+    if prioritize_exact_profile_lexeme {
+        qb.push(" ORDER BY search_tsv @@ websearch_to_tsquery('simple', ");
+        qb.push_bind(&search_text);
+        qb.push(") DESC, rank DESC, created_at DESC, id LIMIT ");
+    } else {
+        qb.push(" ORDER BY rank DESC, created_at DESC, id LIMIT ");
+    }
     qb.push_bind(per_page_actual as i64);
     qb.push(" OFFSET ");
     qb.push_bind(offset);

crates/buzz-search/tests/fts_integration.rs

@@ -303,6 +303,67 @@ async fn kind0_search_by_display_name_works_without_flattening() {
     teardown(pool, &schema).await;
 }
 
+#[tokio::test]
+#[ignore = "requires Postgres"]
+async fn short_kind0_prefix_prioritizes_exact_lexeme_on_a_noisy_page() {
+    let (pool, schema) = setup().await;
+
+    let c = mk_community(&pool, "short-profile-prefix.example").await;
+    let exact_id = rand_bytes32();
+    insert_event(
+        &pool,
+        c,
+        exact_id,
+        rand_bytes32(),
+        0,
+        r#"{"display_name":"jm"}"#,
+        None,
+        1_700_000_000,
+    )
+    .await;
+
+    // These profiles all match jm:* and are newer than the exact name. Without
+    // exact-lexeme priority they consume the entire bounded first page.
+    for (i, display_name) in ["jma", "jmbravo", "jmcharlie", "jmdelta"]
+        .iter()
+        .enumerate()
+    {
+        insert_event(
+            &pool,
+            c,
+            rand_bytes32(),
+            rand_bytes32(),
+            0,
+            &format!(r#"{{"display_name":"{display_name}"}}"#),
+            None,
+            1_700_000_100 + i as i64,
+        )
+        .await;
+    }
+
+    let svc = SearchService::new(pool.clone());
+    let first_page = svc
+        .search(&SearchQuery {
+            community: c,
+            q: "jm".into(),
+            channel_scope: ChannelScope::Any,
+            kinds: Some(vec![0]),
+            authors: None,
+            since: None,
+            until: None,
+            page: 1,
+            per_page: 3,
+            mode: buzz_search::SearchMode::Prefix,
+        })
+        .await
+        .expect("short profile prefix search ok");
+
+    assert_eq!(first_page.hits.len(), 3);
+    assert_eq!(first_page.hits[0].event_id, exact_id);
+
+    teardown(pool, &schema).await;
+}
+
 #[tokio::test]
 #[ignore = "requires Postgres"]
 async fn prefix_mode_matches_final_token_prefix_without_changing_full_text() {