Publish Docker Containers used on CI to GHCR

[MatkovIvan]

Fixes SKIKO-1081 Make docker images for building skiko publicly available

The Skiko project previously used a private Docker registry (registry.jetbrains.team/p/ui/skiko-docker) for build containers, which required secrets for authentication. This prevented CI verification from fork PRs even after manual approval.

The change migrates to GitHub Container Registry (GHCR), making containers publicly accessible and enabling CI to run on fork PRs.

Containers built: https://github.com/orgs/JetBrains/packages?repo_name=skiko

Triggers:

• Push to master: Automatically builds and publishes all Docker images
• Pull requests: Builds images in dry-run mode (no publishing) for verification
• Manual workflow dispatch: Option to publish or just build
• File changes: Triggers on changes to skiko/docker/** or the workflow itself

[igordmn]

Needs also @kropp approval

[eymar]

Cool!