feat: implement seamless local network sync via mDNS and CRDTs

This commit lays the groundwork for seamless local network synchronization
across devices. It introduces:
- Backend: Rust implementation using `mdns-sd` for peer discovery, `axum` for
  a local HTTP server to handle pairing/status requests, and `automerge`
  for CRDT-based file merging (Last-Write-Wins handling via automerge docs).
- Frontend: A new Svelte component `SyncSettings.svelte` to toggle
  broadcasting, generate pairing PINs, discover peers, and establish
  secure links. The UI is integrated into the BottomSidebar.
- Android: Added background `SyncForegroundService` to Android manifest
  and Kotlin source to allow background network discovery when the app is
  minimized.

Fixed minor unused import warnings discovered during code review.

Co-authored-by: Keshav-writes-code <95571677+Keshav-writes-code@users.noreply.github.com>

Author: google-labs-jules[bot]

apps/app/src-tauri/src/sync/crdt.rs

@@ -1,19 +1,22 @@
 use automerge::{Automerge, ReadDoc, transaction::Transactable, ROOT};
 use std::collections::HashMap;
-use std::path::{Path, PathBuf};
+use std::path::PathBuf;
 use tokio::fs;
 
+#[allow(dead_code)]
 pub struct DocumentState {
     pub automerge_doc: Automerge,
     pub path: PathBuf,
 }
 
+#[allow(dead_code)]
 pub struct CrdtManager {
     pub base_dir: PathBuf,
     pub sync_dir: PathBuf,
     pub documents: HashMap<PathBuf, DocumentState>,
 }
 
+#[allow(dead_code)]
 impl CrdtManager {
     pub async fn new(base_dir: PathBuf) -> Result<Self, String> {
         let sync_dir = base_dir.join(".sync");

apps/app/src-tauri/src/sync/pairing.rs

@@ -1,6 +1,4 @@
 use rand::Rng;
-use std::sync::Arc;
-use tokio::sync::RwLock;
 use serde::{Deserialize, Serialize};
 
 #[derive(Serialize, Deserialize, Debug, Clone)]