Support shared spaces (real-time collaboration) for the SageMaker AI - Code Editor

### Product Version

- [ ] Amazon SageMaker Studio Classic
- [x] Amazon SageMaker Studio
- [ ] It is not related to SageMaker Studio

### Product Category

Other

### Description

# Problem Statement

Currently, SageMaker supports **shared spaces** for collaborative work in **JupyterLab / Studio notebooks**, allowing multiple users to edit, run, and manage content in a shared environment.
However, it appears that the same shared-space functionality is **not yet supported in the Code Editor** (VS Code–style interface) in SageMaker Studio / Unified Studio.

See related AWS Re:Post discussion:
🔗 [SageMaker Code Editor – Shared Space](https://repost.aws/questions/QUjGBx3FNzQRi-2UieswBUeQ/sagemaker-code-editor-shared-space)

This limitation means that teams who prefer to use the Code Editor (for Python modules, pipelines, configuration, etc.) cannot collaborate in real time within the same space — reducing the utility of Code Editor for team workflows.

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## Proposed Feature

Add **shared space support for Code Editor**, enabling real-time collaboration similar to notebooks:

- Allow multiple users to open and edit files simultaneously in the same Code Editor space
- Show live cursors, edits, and synchronization across users
- Manage permissions and access via existing space-level controls (shared vs private)
- Maintain shared environment configuration and dependencies consistently for all collaborators
- Add an option when creating or launching a Code Editor space to enable “shared collaboration mode”
- Reflect shared Code Editor spaces in Studio’s UI and via API (list, permissions, metadata, etc.)

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## Use Cases / Benefits

- Enables **real-time collaboration** for teams of ML engineers and data scientists working in Code Editor
- Facilitates **pair programming, live debugging, and code reviews** directly inside SageMaker Studio
- Maintains parity with the **notebook shared-space** experience, simplifying the overall mental model
- Encourages teams to use Code Editor as a full collaborative IDE within the SageMaker ecosystem

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## Additional Context

- The [SageMaker Spaces documentation](https://docs.aws.amazon.com/sagemaker/latest/dg/studio-updated-spaces.html) mentions Code Editor as an application type, but **shared spaces** currently focus on JupyterServer.
- [Shared spaces documentation](https://docs.aws.amazon.com/sagemaker/latest/dg/domain-space.html) does not mention Code Editor explicitly.
- This feature would unify collaboration capabilities across all SageMaker Studio apps (Jupyter, Code Editor, etc.).

The issue names no repository files, tests, or implementation entry points. Start by locating the Code Editor and shared-space integration in the SageMaker project, then determine the existing space, permission, UI, and API boundaries; done means shared Code Editor spaces support synchronized collaboration and are represented consistently in Studio and its API.

Written by the indexing model from the issue text.