Port Brave Sync server to Rust

Use SQLite for persistence and generate Rust protobuf bindings at build time.

Add Docker image support for containerized deployment.

Co-Authored-By: codex <[email protected]>

build.rs

@@ -0,0 +1,21 @@
+use std::{env, path::PathBuf};
+
+fn main() -> Result<(), Box<dyn std::error::Error>> {
+    let proto_dir = PathBuf::from("schema/protobuf/sync_pb");
+    let mut protos = Vec::new();
+    for entry in std::fs::read_dir(&proto_dir)? {
+        let path = entry?.path();
+        if path.extension().is_some_and(|ext| ext == "proto") {
+            println!("cargo:rerun-if-changed={}", path.display());
+            protos.push(path);
+        }
+    }
+
+    let protoc = protoc_bin_vendored::protoc_bin_path()?;
+    unsafe {
+        env::set_var("PROTOC", protoc);
+    }
+
+    prost_build::Config::new().compile_protos(&protos, &[proto_dir])?;
+    Ok(())
+}