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/handlers/feed.rs

@@ -1,8 +1,8 @@
 use std::time::Duration;
 
+use axum::Json;
 use axum::extract::{Query, State};
 use axum::http::HeaderMap;
-use axum::Json;
 use chrono::{DateTime, Utc};
 use serde::{Deserialize, Serialize};
 use uuid::Uuid;
@@ -130,7 +130,11 @@ pub async fn feed(
 
     let has_more = rows.len() as i64 > limit;
     let rows: Vec<FeedRow> = rows.into_iter().take(limit as usize).collect();
-    let next_cursor = if has_more { rows.last().map(|r| r.id) } else { None };
+    let next_cursor = if has_more {
+        rows.last().map(|r| r.id)
+    } else {
+        None
+    };
 
     // Batch check which uploads the current user has liked
     let upload_ids: Vec<Uuid> = rows.iter().map(|r| r.id).collect();
@@ -327,12 +331,11 @@ pub async fn hashtags(
     State(state): State<AppState>,
     auth: AuthUser,
 ) -> Result<Json<Vec<HashtagCount>>, AppError> {
-    let rows: Vec<(String, i64)> = sqlx::query_as(
-        "SELECT tag, upload_count FROM v_hashtag_counts WHERE event_id = $1",
-    )
-    .bind(auth.event_id)
-    .fetch_all(&state.pool)
-    .await?;
+    let rows: Vec<(String, i64)> =
+        sqlx::query_as("SELECT tag, upload_count FROM v_hashtag_counts WHERE event_id = $1")
+            .bind(auth.event_id)
+            .fetch_all(&state.pool)
+            .await?;
 
     Ok(Json(
         rows.into_iter()
@@ -362,14 +365,13 @@ async fn get_liked_set(
     if upload_ids.is_empty() {
         return std::collections::HashSet::new();
     }
-    let rows: Vec<(Uuid,)> = sqlx::query_as(
-        "SELECT upload_id FROM \"like\" WHERE user_id = $1 AND upload_id = ANY($2)",
-    )
-    .bind(user_id)
-    .bind(upload_ids)
-    .fetch_all(pool)
-    .await
-    .unwrap_or_default();
+    let rows: Vec<(Uuid,)> =
+        sqlx::query_as("SELECT upload_id FROM \"like\" WHERE user_id = $1 AND upload_id = ANY($2)")
+            .bind(user_id)
+            .bind(upload_ids)
+            .fetch_all(pool)
+            .await
+            .unwrap_or_default();
 
     rows.into_iter().map(|r| r.0).collect()
 }