Update HaaLeo/publish-vscode-extension when Node 24 version is available

[zackverham]

Context

Part of #4115 — updating GitHub Actions that use deprecated Node.js 20.

HaaLeo/publish-vscode-extension@v2 still uses Node 20 and there is no newer release with Node 24 support. This action is used in publish.yaml for publishing to both the VS Marketplace and Open VSX Registry.

Action needed

• Monitor https://github.com/HaaLeo/publish-vscode-extension for a new release that uses Node 24.
• Once available, update the two usages in .github/workflows/publish.yaml (lines 41 and 69).

Deadline

GitHub will force Node.js 24 starting June 2, 2026. Node.js 20 will be removed from runners on September 16, 2026.

Alternatives if upstream doesn't update in time

• Replace with direct vsce publish and ovsx publish CLI commands.
• Set FORCE_JAVASCRIPT_ACTIONS_TO_NODE24=true env var as a temporary workaround.