refactor: combine Docker and npm publish into single workflow

Merges docker-publish.yml and npm-publish.yml into publish.yml with
three parallel jobs: check-version, docker, and npm. Removes redundant
host-side build from docker job and adds pnpm caching to npm job.

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

Author: tianzhou

.github/workflows/deploy-demo.yml

@@ -2,7 +2,7 @@ name: Deploy Demo
 
 on:
   workflow_run:
-    workflows: ["Publish to Docker Hub"]
+    workflows: ["Publish"]
     types: [completed]
     branches: [main]