Update docs packaging and README

[freakdaniel]

Summary

Fix the documentation site artifact layout so GitHub Pages serves it at /Hyprism/docs/. Update public documentation links and deployment instructions

Type of Change

• Bug fix
• Documentation update
• Build / CI changes

Changes

• Build and serve the static site from out/docs, removing the duplicated project directory from the Pages artifact
• Update documentation links in the README and GitHub issue templates
• Align the English and Russian publishing instructions with the GitHub Pages project path
• Refresh the README docs badge and tidy contributor and support links

Checklist

• Code follows the project's style and conventions
• Self-reviewed the diff before submitting
• No unintended files are included (build artifacts, local configs, etc.)
• Documentation updated if needed