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]>

schema/protobuf/sync_pb/loopback_server.proto

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+// Copyright 2012 The Chromium Authors
+// Use of this source code is governed by a BSD-style license that can be
+// found in the LICENSE file.
+//
+// Sync protocol for persisting the loopback server state to disk.
+
+syntax = "proto2";
+
+option go_package = "./sync_pb";
+
+option java_multiple_files = true;
+option java_package = "org.chromium.components.sync.protocol";
+
+option optimize_for = LITE_RUNTIME;
+
+package sync_pb;
+
+import "sync_entity.proto";
+
+// Serialization of the LoopbackServerEntity and its ancestors.
+message LoopbackServerEntity {
+  // Entity type mapping to one of the subclasses of LoopbackServerEntity.
+  enum Type {
+    UNKNOWN = 0;
+    BOOKMARK = 1;
+    PERMANENT = 2;
+    TOMBSTONE = 3;
+    UNIQUE = 4;
+  }
+
+  optional Type type = 1;
+  optional SyncEntity entity = 2;
+  optional int64 model_type = 3;
+}
+
+// Contains the loopback server state.
+message LoopbackServerProto {
+  // The protocol buffer format version.
+  optional int64 version = 1;
+
+  optional int64 store_birthday = 2;
+
+  repeated LoopbackServerEntity entities = 3;
+
+  // All Keystore keys known to the server.
+  repeated bytes keystore_keys = 4;
+
+  // The last entity ID that was assigned to an entity.
+  optional int64 last_version_assigned = 5;
+}