chore(registry): use docker-public registry path

Update image references from registry.zeidler.dev/docker/playground to
registry.zeidler.dev/docker-public/playground in docker-compose.yml and build.sh.
Also bind-mount ${HOME}/.claude instead of using the claude-config named volume.

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

build.sh

@@ -4,7 +4,7 @@
 set -euo pipefail
 
 SCRIPT_DIR="$(cd "$(dirname "${BASH_SOURCE[0]}")" && pwd)"
-REGISTRY="registry.zeidler.dev/docker/playground"
+REGISTRY="registry.zeidler.dev/docker-public/playground"
 TAG="${IMAGE_TAG:-latest}"
 
 GREEN='\033[0;32m'; NC='\033[0m'

docker-compose.yml

@@ -3,7 +3,7 @@ services:
   # Bridges the isolated internal network to the internet.
   # Enforces an egress allowlist — see proxy/squid.conf.
   proxy:
-    image: registry.zeidler.dev/docker/playground/docker-claude-proxy:${IMAGE_TAG:-latest}
+    image: registry.zeidler.dev/docker-public/playground/docker-claude-proxy:${IMAGE_TAG:-latest}
     networks:
       - claude-internal # reachable by claude and webui containers
       - proxy-external # has outbound internet access
@@ -22,7 +22,7 @@ services:
   # No direct internet access. All egress routes through the proxy sidecar.
   # Run via "docker compose run --rm --service-ports claude" (managed by claude.sh).
   claude:
-    image: registry.zeidler.dev/docker/playground/docker-claude-claude:${IMAGE_TAG:-latest}
+    image: registry.zeidler.dev/docker-public/playground/docker-claude-claude:${IMAGE_TAG:-latest}
     depends_on:
       proxy:
         condition: service_healthy
@@ -46,7 +46,7 @@ services:
       # OAuth callback — required for browser-based login (claude login)
       - "0.0.0.0:54545:54545"
     volumes:
-      - claude-config:/home/node/.claude
+      - ${HOME}/.claude:/home/node/.claude
       # Workspace is injected by claude.sh via --volume flag at run time (current directory).
     security_opt:
       - no-new-privileges:true
@@ -60,7 +60,7 @@ services:
   # Protected by HTTP basic auth — set WEBUI_USER / WEBUI_PASSWORD in .env.
   # Network isolation is identical to the CLI container.
   webui:
-    image: registry.zeidler.dev/docker/playground/docker-claude-claude:${IMAGE_TAG:-latest}
+    image: registry.zeidler.dev/docker-public/playground/docker-claude-claude:${IMAGE_TAG:-latest}
     entrypoint: ["/usr/local/bin/webui-entrypoint.sh"]
     depends_on:
       proxy: