feat: unique display names (case-insensitive) + inline recover on join

Backend:
- Migration 007 deduplicates existing users by name (case-insensitive,
  keeping oldest) and adds a unique index on (event_id, LOWER(display_name))
- find_by_event_and_name is now case-insensitive (LOWER comparison)
- join endpoint checks name availability before creating; returns 409
  Conflict with code "conflict" when the name is taken

Frontend (join page):
- On 409, switches to a name-taken view showing an amber warning with
  name-choice tips, a PIN input that runs the recover flow inline, and
  an "Anderen Namen wählen" button that returns to the name input

Test guide: added Steps 8 (rate-limit auto-retry) and 9 (name uniqueness)

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

backend/migrations/007_user_name_unique.down.sql

@@ -0,0 +1,4 @@
+DROP INDEX IF EXISTS idx_user_event_name_ci;
+
+CREATE INDEX idx_user_event_name
+    ON "user"(event_id, display_name);

backend/migrations/007_user_name_unique.up.sql

@@ -0,0 +1,15 @@
+-- Deduplicate users with the same name (case-insensitive) per event,
+-- keeping the oldest account so no real data is lost.
+DELETE FROM "user"
+WHERE id NOT IN (
+    SELECT DISTINCT ON (event_id, LOWER(display_name)) id
+    FROM "user"
+    ORDER BY event_id, LOWER(display_name), created_at ASC
+);
+
+-- Drop the old non-unique index (replaced below)
+DROP INDEX IF EXISTS idx_user_event_name;
+
+-- Unique index enforces one account per name per event (case-insensitive)
+CREATE UNIQUE INDEX idx_user_event_name_ci
+    ON "user" (event_id, LOWER(display_name));

backend/src/auth/handlers.rs

@@ -57,6 +57,14 @@ pub async fn join(
     )
     .await?;
 
+    // Reject if a user with this name (case-insensitive) already exists
+    if User::name_taken(&state.pool, event.id, display_name).await? {
+        return Err(AppError::Conflict(format!(
+            "Der Name \"{}\" ist bereits vergeben.",
+            display_name
+        )));
+    }
+
     // Generate a 4-digit PIN
     let pin: String = format!("{:04}", rand::rng().random_range(0..10000u32));
     let pin_hash =

backend/src/models/user.rs

@@ -59,7 +59,7 @@ impl User {
         display_name: &str,
     ) -> Result<Vec<Self>, sqlx::Error> {
         sqlx::query_as::<_, Self>(
-            "SELECT * FROM \"user\" WHERE event_id = $1 AND display_name = $2",
+            "SELECT * FROM \"user\" WHERE event_id = $1 AND LOWER(display_name) = LOWER($2)",
         )
         .bind(event_id)
         .bind(display_name)
@@ -67,6 +67,21 @@ impl User {
         .await
     }
 
+    pub async fn name_taken(
+        pool: &PgPool,
+        event_id: Uuid,
+        display_name: &str,
+    ) -> Result<bool, sqlx::Error> {
+        let row: (bool,) = sqlx::query_as(
+            "SELECT EXISTS(SELECT 1 FROM \"user\" WHERE event_id = $1 AND LOWER(display_name) = LOWER($2))",
+        )
+        .bind(event_id)
+        .bind(display_name)
+        .fetch_one(pool)
+        .await?;
+        Ok(row.0)
+    }
+
     pub async fn increment_failed_pin(pool: &PgPool, id: Uuid) -> Result<i16, sqlx::Error> {
         let row: (i16,) = sqlx::query_as(
             "UPDATE \"user\"