#45 feat: implement seamless local network sync via mDNS and CRDTs

[Anonymous]

Originally created by: Keshav-writes-code

Implements the Apple-like seamless local network sync feature for Markdown notes.

Features

1. Device Discovery & Pairing: Uses mDNS (mdns-sd crate) to broadcast and discover instances of the application on the local network. A simple 6-digit PIN mechanism authenticates and establishes trust between devices.
2. Conflict Resolution: Integrates the automerge crate to manage files using Conflict-free Replicated Data Types (CRDTs). The app projects CRDT history to the visible .md files and maintains a hidden .sync/ directory for metadata.
3. Background Sync (Android): Implements an Android ForegroundService to keep the sync process alive in the background.
4. Local Network API: Runs a lightweight axum HTTP server within the Rust backend to exchange pairing statuses and (eventually) CRDT payloads.
5. Frontend Settings: Adds a "Sync Devices" modal to the sidebar that allows users to enable/disable the feature, view their PIN, and connect to discovered peers.

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PR created automatically by Jules for task 6380593602282876537 started by @Keshav-writes-code

[Anonymous]

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