Wire node-static deploy for chat_web_app (closes #13).

Add build:prod/beta webroot scripts, Gitea CI/deploy workflows, and bake API
URLs from REACT_APP_* so hosts can deploy via server-infra like dta_webapp.

.gitea/workflows/deploy-prod.yml

@@ -0,0 +1,22 @@
+name: Deploy Prod
+
+# Runs after Unit Tests completes on master. Direct pushes only (not PRs).
+on:
+  workflow_run:
+    workflows: [Unit Tests]
+    types: [completed]
+    branches: [master]
+
+jobs:
+  deploy:
+    if: gitea.event.workflow_run.conclusion == 'success' && gitea.event.workflow_run.event == 'push'
+    runs-on: self-hosted
+    env:
+      SERVER_INFRA_ROOT: /home/westfarn/Documents/repos/server-infra
+    steps:
+      - name: Deploy chat_web_app prod
+        run: |
+          "$SERVER_INFRA_ROOT/scripts/deploy.sh" \
+            --app chat_web_app \
+            --env prod \
+            --ref "${{ gitea.event.workflow_run.head_sha }}"