Add live syncback functionality and optimize service encoding

- Introduced a new endpoint `/api/syncback` for one-click full sync from Roblox Studio to the filesystem, eliminating the need for an active WebSocket connection.
- Implemented `SyncbackRequest` and `ServiceChunk` structures to handle service-level properties and child instances during syncback.
- Enhanced `encodeService` to include ObjectValue carriers for accurate reference handling and prevent data loss.
- Updated the syncback process to utilize Luau-style relative paths for reference attributes, improving path management and consistency.
- Integrated session caching in the matching algorithm to optimize performance during syncback operations.

These changes significantly improve the live syncback experience, ensuring reliable data synchronization and enhanced performance during development.

.cursor/rules/atlas-plugin.mdc

@@ -25,9 +25,10 @@ Built with Roact (React-like), handles WebSocket sync with server, patch applica
   - `Studio/` - Studio API wrappers (`StudioPluginAction`, `StudioPluginContext`, `StudioPluginGui`, `StudioToggleButton`, `StudioToolbarContext`, `StudioToolbar`)
   - General: `Header`, `TextInput`, `TextButton`, `Checkbox`, `Dropdown`, `Tag`, `IconButton`, `Tooltip`, `TouchRipple`, `VirtualScroller`, `ScrollingFrame`, `Spinner`, `BorderedContainer`, `EditableImage`, `SlicedImage`, `ClassIcon`
 - **StatusPages/** - Main UI pages
-  - `NotConnected.lua` - Connection form (host/port input)
+  - `NotConnected.lua` - Connection form (host/port input), "Syncback" button (Danger style)
   - `Connecting.lua` - Loading screen
   - `Confirming.lua` - Patch confirmation dialog with push/pull/ignore per-node selections
+  - `SyncbackConfirm` - Floating dialog for live syncback confirmation (rendered by `App/init.lua`)
   - `Connected.lua` - Status display with patch history
   - `Error.lua` - Error display
   - `Settings/` - Settings UI (`init.lua`, `Setting.lua`)
@@ -56,7 +57,8 @@ Built with Roact (React-like), handles WebSocket sync with server, patch applica
 - **init.lua** - Main batcher: accumulates changes every 200ms, pause/resume, deferred Ref resolution
 - **createPatchSet.lua** - Converts pending changes to PatchSet
 - **encodePatchUpdate.lua** - Encodes property updates including Ref properties via InstanceMap
-- **encodeInstance.lua** - Full instance encoding (for additions/syncback)
+- **encodeInstance.lua** - Full instance encoding (for additions/syncback); includes duplicate detection helpers (`findDuplicateNames`, `hasDuplicateSiblings`, `isPathUnique`)
+- **encodeService.lua** - Encodes service-level properties/attributes/refs for live syncback; uses ObjectValue carriers for Ref properties
 - **encodeProperty.lua** - Single property value encoding via RbxDom
 - **propertyFilter.lua** - Property type filtering (only `UniqueId` blocked; `Ref` is allowed)
 
@@ -242,12 +244,22 @@ Pairs incoming virtual instances with existing Studio instances during hydration
 
 **Algorithm:**
 1. **Fast path:** Group by (Name, ClassName). 1:1 groups get instant-matched with zero scoring.
-2. **Ambiguous groups:** For groups with multiple candidates, compute pairwise `_computeChangeCount()` (recursive, scores entire subtree). Greedy assignment sorted by cost ascending, child-order tiebreaker for stability.
+2. **Ambiguous groups:** For groups with multiple candidates, compute pairwise `computePairCost()` (recursive, scores entire subtree). Greedy assignment sorted by cost ascending, child-order tiebreaker for stability.
 3. **Leftovers:** Unmatched virtual = new instances, unmatched studio = deleted.
 
+**Performance:** File-level `--!native` and `--!optimize 2` directives for native codegen. `MatchingSession` caches results across recursive calls:
+```lua
+type MatchingSession = {
+    matchCache: { [string]: { [Instance]: MatchResult } },
+    costCache: { [string]: { [Instance]: number } },
+}
+```
+
+**Valid children tracking:** `cacheVirtual()` filters children to only those existing in `virtualInstances`, preventing crashes on incomplete virtual instance trees.
+
 **Sort stability note:** `table.sort` is NOT stable in Luau. Comparator breaks ties by insertion index to ensure deterministic ordering.
 
-**Value equality:** Shared `trueEquals.lua` module used by both `matching.lua` and `diff.lua` -- fuzzy equality for floats (epsilon 0.0001), Color3 via RGB ints, CFrame/Vector3 component-wise, NaN handling, nil/null-ref equivalence.
+**Value equality:** Shared `trueEquals.lua` module used by both `matching.lua` and `diff.lua` -- fuzzy equality for floats (epsilon 0.0001, absolute + relative), Color3 via RGB ints, CFrame/Vector3 component-wise, NaN handling, nil/null-ref equivalence, EnumItem/number interop.
 
 ## InstanceMap (`InstanceMap.lua`)
 
@@ -308,6 +320,29 @@ Watches Studio changes and sends them to the server in real-time. Enabled by def
 - `__paused` flag blocks flushes during confirmation dialog
 - `RunService:IsRunning()` blocks during Play mode
 
+## Live Syncback
+
+One-click full sync from Studio to filesystem. Available from the **NotConnected page** -- does not require an active WebSocket session. Sends directly to the server via HTTP POST using the host/port fields from the connection form.
+
+**`SYNCBACK_SERVICES` constant (14 services):** Lighting, MaterialService, ReplicatedFirst, ReplicatedStorage, ServerScriptService, ServerStorage, SoundService, StarterGui, StarterPack, StarterPlayer, Teams, TextChatService, VoiceChatService, Workspace.
+
+**Flow:**
+1. User clicks "Syncback" button on NotConnected page → `SyncbackConfirm` floating dialog appears
+2. Dialog warns: "This will overwrite your project files with the current Studio state. This cannot be undone."
+3. User confirms → `performSyncback()`:
+   a. Iterates `SYNCBACK_SERVICES`, calls `encodeService(service)` for each
+   b. Collects all children instances and ObjectValue Ref carriers
+   c. Serializes all children via `SerializationService:SerializeInstancesAsync()` into a single buffer
+   d. Destroys temporary ObjectValue carriers
+   e. POSTs to `http://host:port/api/syncback` (MessagePack): `{protocolVersion, serverVersion, placeId, data, services}`
+4. Shows success/error notification
+
+**`encodeService(service)`** (`ChangeBatcher/encodeService.lua`):
+- Encodes service-level properties via `RbxDom.findClassDescriptor()`
+- Skips: `Parent`, `Name`, `Archivable`, `Attributes`, `Tags` (handled separately), class-specific excludes (`Lighting.ClockTime`)
+- Ref properties: creates temporary `ObjectValue` carriers (Name = property name, Value = target instance), stores 1-based index in `refs` map
+- Returns `(chunk, refTargets)` where `chunk = {className, childCount, refTargetCount, properties?, refs?}`
+
 ## Dependencies
 
 ### Vendored Packages (`plugin/Packages/`)