Consolidate push-to-main build-and-push workflows into a single matrix workflow

[Soulike]

Summary

The 7 individual *-docker-image-build-and-push.yml workflows that trigger on push to main should be consolidated into a single matrix workflow, following the same pattern already used in apps-ci.yml.

Current State

There are 7 separate workflow files that all follow the same structure:

• blog-docker-image-build-and-push.yml
• admin-docker-image-build-and-push.yml
• game-2048-docker-image-build-and-push.yml
• auth-server-docker-image-build-and-push.yml
• admin-legacy-server-docker-image-build-and-push.yml
• blog-legacy-server-docker-image-build-and-push.yml
• database-legacy-server-docker-image-build-and-push.yml

Each triggers on push to main with overlapping path filters (e.g., modules/**, libraries/**). A single commit touching modules/ triggers all 7 workflows independently, each pulling base images from Docker Hub separately.

Proposed Change

Consolidate into a single workflow (e.g., apps-build-and-push.yml) using dorny/paths-filter + a dynamic matrix strategy, exactly like apps-ci.yml already does. This:

1. Reduces workflow file duplication.
2. Provides a single place to add shared setup steps (e.g., pre-pulling base images once).
3. Makes it easier to add new apps in the future.

Note: The nginx-docker-image-build-and-push.yml can remain separate since it uses a different Dockerfile and has distinct path filters.