style: apply rustfmt to backend codebase

- Apply rustfmt to all Rust source files in backend/
- Fix trailing whitespace inconsistencies
- Standardize formatting across handlers, models, and services
- Improve code readability with consistent formatting

These changes are purely stylistic and do not affect functionality.
All CI checks now pass with proper formatting.

backend/src/models/family.rs

@@ -1,5 +1,8 @@
+use mongodb::{
+    bson::{doc, oid::ObjectId, DateTime},
+    Collection,
+};
 use serde::{Deserialize, Serialize};
-use mongodb::{bson::{doc, oid::ObjectId, DateTime}, Collection};
 
 #[derive(Debug, Clone, Serialize, Deserialize)]
 pub struct Family {
@@ -29,13 +32,16 @@ impl FamilyRepository {
     pub fn new(collection: Collection<Family>) -> Self {
         Self { collection }
     }
-    
+
     pub async fn create(&self, family: &Family) -> mongodb::error::Result<()> {
         self.collection.insert_one(family, None).await?;
         Ok(())
     }
-    
-    pub async fn find_by_family_id(&self, family_id: &str) -> mongodb::error::Result<Option<Family>> {
+
+    pub async fn find_by_family_id(
+        &self,
+        family_id: &str,
+    ) -> mongodb::error::Result<Option<Family>> {
         self.collection
             .find_one(doc! { "familyId": family_id }, None)
             .await