refactor: reorganize project into monorepo with frontend scaffolding

Convert project from single backend to monorepo structure with separate
frontend (Vue 3 + TypeScript + Vite) and backend directories. Updates
all configuration files and build system to support both workspaces.

Ref: T007 (specs/001-modbus-relay-control)

backend/src/infrastructure/persistence/mod.rs

@@ -0,0 +1,7 @@
+//! Persistence layer implementations.
+//!
+//! This module contains the concrete implementations of repository traits
+//! for data persistence, including SQLite-based storage for relay labels.
+
+/// `SQLite` repository implementation for relay labels.
+pub mod sqlite_repository;

backend/src/infrastructure/persistence/sqlite_repository.rs

@@ -0,0 +1,64 @@
+use sqlx::SqlitePool;
+
+use crate::domain::relay::repository::RepositoryError;
+
+/// `SQLite` implementation of the relay label repository.
+///
+/// This repository manages persistent storage of relay labels using `SQLite`,
+/// with automatic schema migrations via `SQLx`.
+pub struct SqliteRelayLabelRepository {
+    /// The `SQLite` connection pool for database operations.
+    pool: SqlitePool,
+}
+
+impl SqliteRelayLabelRepository {
+    /// Creates a new `SQLite` relay label repository.
+    ///
+    /// # Arguments
+    ///
+    /// * `db_path` - The `SQLite` database path or connection string (e.g., `"sqlite://data.db"`)
+    ///
+    /// # Errors
+    ///
+    /// Returns `RepositoryError::DatabaseError` if the connection fails or migrations cannot be applied.
+    pub async fn new(db_path: &str) -> Result<Self, RepositoryError> {
+        let pool = SqlitePool::connect(db_path)
+            .await
+            .map_err(|e| RepositoryError::DatabaseError(e.to_string()))?;
+        let repo = Self { pool };
+        repo.run_migrations().await?;
+        Ok(repo)
+    }
+
+    /// Returns a reference to the underlying connection pool.
+    ///
+    /// This is primarily used for testing to verify schema and constraints.
+    #[must_use]
+    pub const fn pool(&self) -> &SqlitePool {
+        &self.pool
+    }
+
+    /// Creates a new in-memory `SQLite` relay label repository.
+    ///
+    /// This is useful for testing and ephemeral data storage.
+    ///
+    /// # Errors
+    ///
+    /// Returns `RepositoryError::DatabaseError` if the in-memory database cannot be created.
+    pub async fn in_memory() -> Result<Self, RepositoryError> {
+        Self::new("sqlite::memory:").await
+    }
+
+    /// Runs all pending database migrations.
+    ///
+    /// # Errors
+    ///
+    /// Returns `RepositoryError::DatabaseError` if migrations fail to apply.
+    async fn run_migrations(&self) -> Result<(), RepositoryError> {
+        sqlx::migrate!("../migrations/")
+            .run(&self.pool)
+            .await
+            .map_err(|e| RepositoryError::DatabaseError(e.to_string()))?;
+        Ok(())
+    }
+}