style(backend): rustfmt the whole tree; gate cargo fmt --check in CI

The backend had never been run through rustfmt. Doing it in one mechanical pass (134 files)
so no future functional diff is buried under formatting churn, then gating `cargo fmt
--check` in checks.yml so it stays clean.

Formatting only — no logic, SQL, or behaviour changed. Verified after the reformat:
cargo test 56 passed, clippy --all-targets -D warnings clean, cargo fmt --check clean.

This is the deferred cleanup noted when CI's Format step was first left out.

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

backend/src/models/comment.rs

@@ -83,12 +83,10 @@ impl Comment {
     }
 
     pub async fn find_by_id(pool: &PgPool, id: Uuid) -> Result<Option<Self>, sqlx::Error> {
-        sqlx::query_as::<_, Self>(
-            "SELECT * FROM comment WHERE id = $1 AND deleted_at IS NULL",
-        )
-        .bind(id)
-        .fetch_optional(pool)
-        .await
+        sqlx::query_as::<_, Self>("SELECT * FROM comment WHERE id = $1 AND deleted_at IS NULL")
+            .bind(id)
+            .fetch_optional(pool)
+            .await
     }
 
     /// Event-scoped soft delete. Returns `false` if the comment doesn't exist or belongs to a

backend/src/models/event.rs

@@ -33,13 +33,11 @@ impl Event {
     }
 
     pub async fn create(pool: &PgPool, slug: &str, name: &str) -> Result<Self, sqlx::Error> {
-        sqlx::query_as::<_, Self>(
-            "INSERT INTO event (slug, name) VALUES ($1, $2) RETURNING *",
-        )
-        .bind(slug)
-        .bind(name)
-        .fetch_one(pool)
-        .await
+        sqlx::query_as::<_, Self>("INSERT INTO event (slug, name) VALUES ($1, $2) RETURNING *")
+            .bind(slug)
+            .bind(name)
+            .fetch_one(pool)
+            .await
     }
 
     pub async fn find_or_create(

backend/src/models/hashtag.rs

@@ -122,14 +122,20 @@ mod tests {
         assert_eq!(extract_hashtags(&format!("#{ok}")), vec![ok.clone()]);
         // 41+ chars → dropped entirely (not truncated).
         let too_long = "a".repeat(41);
-        assert_eq!(extract_hashtags(&format!("#{too_long}")), Vec::<String>::new());
+        assert_eq!(
+            extract_hashtags(&format!("#{too_long}")),
+            Vec::<String>::new()
+        );
     }
 
     #[test]
     fn duplicate_tags_are_returned_verbatim_not_deduplicated() {
         // Dedup is the DB's job (Hashtag::upsert ON CONFLICT); extraction returns each
         // occurrence so callers can count/link them independently. Case folds to lower.
-        assert_eq!(extract_hashtags("#fun #Fun #fun!"), vec!["fun", "fun", "fun"]);
+        assert_eq!(
+            extract_hashtags("#fun #Fun #fun!"),
+            vec!["fun", "fun", "fun"]
+        );
     }
 
     #[test]

backend/src/models/session.rs

@@ -90,10 +90,7 @@ impl Session {
         Ok(())
     }
 
-    pub async fn delete_by_token_hash(
-        pool: &PgPool,
-        token_hash: &str,
-    ) -> Result<(), sqlx::Error> {
+    pub async fn delete_by_token_hash(pool: &PgPool, token_hash: &str) -> Result<(), sqlx::Error> {
         sqlx::query("DELETE FROM session WHERE token_hash = $1")
             .bind(token_hash)
             .execute(pool)

backend/src/models/user.rs

@@ -109,14 +109,16 @@ impl User {
         Ok(row.0)
     }
 
-    pub async fn lock_pin(pool: &PgPool, id: Uuid, until: DateTime<Utc>) -> Result<(), sqlx::Error> {
-        sqlx::query(
-            "UPDATE \"user\" SET pin_locked_until = $2 WHERE id = $1",
-        )
-        .bind(id)
-        .bind(until)
-        .execute(pool)
-        .await?;
+    pub async fn lock_pin(
+        pool: &PgPool,
+        id: Uuid,
+        until: DateTime<Utc>,
+    ) -> Result<(), sqlx::Error> {
+        sqlx::query("UPDATE \"user\" SET pin_locked_until = $2 WHERE id = $1")
+            .bind(id)
+            .bind(until)
+            .execute(pool)
+            .await?;
         Ok(())
     }