feat: REL-11387 dev server context management

[pranjal-jately-ld]

Description

What does this PR do?

This PR implements bidirectional context synchronization between the Developer Toolbar (in Dev Server Mode) and the Dev Server. Previously, context changes were not synchronized.

Changes:

• When context changes in the toolbar (via context selector or JSON editor), it now syncs to the dev server via PATCH /dev/projects/{projectKey} API call
• When context changes in the dev server, it now syncs to the toolbar and updates the active context automatically

Type of Change

• 🐛 Bug fix (non-breaking change that fixes an issue)
• ✨ New feature (non-breaking change that adds functionality)
• 💥 Breaking change (fix or feature that would cause existing functionality to not work as expected)
• 📚 Documentation (changes to documentation only)
• 🔧 Refactor (code change that neither fixes a bug nor adds a feature)
• 🎨 Style (formatting, missing semicolons, etc; no production code change)
• ⚡ Performance (code change that improves performance)
• ✅ Test (adding missing tests, refactoring tests; no production code change)
• 🔨 Chore (updating grunt tasks, build process, etc; no production code change)

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Screenshots/Videos

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Related Jira issue: REL-11387: Update Dev Server Mode context management

[cspath1]

This is looking good! Really excited to see this in place!