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.mdc

@@ -32,6 +32,7 @@ Atlas bridges filesystem and Roblox Studio, enabling professional development to
 - Build/upload rbxl/rbxm files from command line
 - Syncback: pull instances from Roblox → filesystem (7.7.0+)
 - Two-way sync (plugin-based): live bidirectional sync during `atlas serve` sessions
+- Live syncback: one-click full sync from Studio to filesystem during `atlas serve` (no WebSocket connection required)
 
 ### Two-Way Sync Strategy
 
@@ -206,7 +207,7 @@ pub struct InstanceContext {
 }
 ```
 
-**Filename handling:** Instance names with forbidden filesystem chars are slugified (forbidden chars → `_`), deduplicated (`~1`, `~2`, etc. on collision), and the real name is stored in `.meta.json5`/`.model.json5` `name` fields. See `src/syncback/file_names.rs`.
+**Filename handling:** Instance names with forbidden filesystem chars are slugified (forbidden chars → `_`), deduplicated (`~2`, `~3`, etc. on collision), and the real name is stored in `.meta.json5`/`.model.json5` `name` fields. See `src/syncback/file_names.rs`.
 
 **VFS passed separately to snapshot functions:**
 ```rust
@@ -322,6 +323,7 @@ src/                     - Rust server/CLI
     dedup_suffix.rs     - Dedup cleanup rules
     meta.rs             - Meta file read/write helpers
   web/                  - HTTP/WebSocket server
+    interface.rs        - Wire types (patches, syncback requests)
   change_processor.rs   - Two-way sync filesystem writer
   git.rs                - Git integration (changed files, SHA1 hashing, auto-staging)
   rojo_ref.rs           - Ref path system (Rojo_Ref_*, RefPathIndex)
@@ -333,6 +335,7 @@ plugin/src/             - Lua Studio plugin
     matching.lua        - Lua matching algorithm
     trueEquals.lua      - Shared value equality module
   ChangeBatcher/        - Two-way sync patch creation
+    encodeService.lua   - Service-level property encoding for live syncback
   Config.lua            - Version and protocol config
   PatchTree.lua         - Patch visualization tree (git-based default selections)
   SHA1.luau             - SHA1 hash for git blob format comparison