[New Rich Text Editor]: Maintain backward Markdown Compatibility

[habibayman]

❌ This issue is not open for contribution. Visit Contributing guidelines to learn about the contributing process and how to find suitable issues.

Desired behavior

The new Tiptap-based rich text editor currently works with a structured JSON format internally. To replace the old editor across the application, it must be 100% backward compatible with the existing Markdown format.
This requires supporting two things:

• Standard Markdown elements previously handled by the ToastUI editor and its Showdown converter.
• A specific, legacy format for custom nodes, particularly for Images () and Math Formulas ($$...$$).

The goal is to ensure that loading existing Markdown and saving new content from the Tiptap editor results in a format that is indistinguishable from the old system, preventing any data conversion issues or loss of content.

Current behavior

• Component is available for isolated development at http://localhost:8080/editor-dev#/
• All the buttons in the toolbar are fully functioning
• No trace of any save/load logic can be found in the editor

Testing Strategy

Create a fake parent to mimic the content data flow, and create a playground to be able to test the results.
detailed strategy will be found in the PR.