fix(extension): release processing lock after partial_success responses

[VarshithReddy2006]

Summary

This PR fixes a browser extension state-management bug where the processing mutex (isProcessing) could remain locked after a partial publishing result.

When the backend returns partial_success, the background script maps it to warning. The content script previously released the processing lock only for success and error, causing the extension to remain stuck after a warning status.

Changes

• Treat warning as a terminal processing state.
• Release isProcessing for:
  • success
  • error
  • warning

Testing

Manual verification:

1. Configure multiple publishing platforms.
2. Force one platform to succeed and another to fail so the backend returns partial_success.
3. Verify that the extension receives STATUS_UPDATE with status: "warning".
4. Confirm that another blog generation can be started without refreshing the page.

Fixes #217.