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/web_apk_specifics.proto

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+// Copyright 2023 The Chromium Authors
+// Use of this source code is governed by a BSD-style license that can be
+// found in the LICENSE file.
+
+// If you change or add any fields in this file, update
+// components/sync/protocol/proto_visitors.h and potentially
+// components/sync/protocol/proto_enum_conversions.{h, cc}.
+
+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;
+
+// Sync & local data: Information about web app icon.
+message WebApkIconInfo {
+  enum Purpose {
+    UNSPECIFIED = 0;
+    // Suitable for any purpose.
+    ANY = 1;
+    // Designed for masking.
+    MASKABLE = 2;
+    // Suitable for monochrome purposes.
+    MONOCHROME = 3;
+  }
+
+  // The size of the square app icon, in raw pixels.
+  optional int32 size_in_px = 1;
+  // The URL of the app icon.
+  optional string url = 2;
+  // The purpose or context in which the icon should be used.
+  optional Purpose purpose = 3;
+}
+
+// WebApk data.
+message WebApkSpecifics {
+  optional string manifest_id = 1;
+  optional string start_url = 2;
+  optional string name = 3;
+  optional uint32 theme_color = 4;
+  optional string scope = 5;
+  repeated WebApkIconInfo icon_infos = 6;
+
+  // Time when this WebApk was last used or installed.
+  // Number of microseconds since 1601, aka Windows epoch.
+  optional int64 last_used_time_windows_epoch_micros = 7;
+}