Publish VSCode extension on open-vsx.org

[zygoloid]

In addition to publishing our extension on the official VS Code marketplace, it would be useful to publish it on open-vsx.org so that VS Code-compatible IDEs like VSCodium, Cursor, and Antigravity can use the extension too.

[TechWizard9999]

Hi @zygoloid, Please check it once!

I have implemented and tested the Open VSX publishing workflow in PR #6773.

Testing Performed:

• package.json: ovsx package added as a dev dependency (^0.10.0).
• Built VSIX: Validated successful packaging via npx vsce package.
• CLI Check: Verified ovsx publish functionality locally.
• Workflow YAML structure: Validated the dual-publishing setup (workflow_dispatch with target selection, proper pemissions, steps, and egress rules).

Everything is packaged correctly and ready to merge!

[jonmeow]

A maintainer probably needs to handle this in order to ensure account and information is set up correctly on Open VSX. Also, I think we should probably use a manual push initially, not a GitHub action.

[cjdb]

The extension has been uploaded to https://open-vsx.org/extension/carbon-lang/carbon-vscode. Next steps:

• Ensure Claiming namespace carbon-lang EclipseFdn/open-vsx.org#9363 is resolved
• Set up a GitHub workflow to automate update publication