feat: dashboard UX optimization + real-time backend stats + health probe fix + pool shuffle

- dashboard.html: major UX overhaul (+657/-308 lines)
- server.py: /api/admin/backends now returns real-time RPM and model_count
- pool_manager.py: random.shuffle backends for load distribution
- config.py: health probe endpoint /v1/models → /models
- docker-compose.yml: add SIDECAR_PRIMARY_WAIT_MAX_RETRIES=6

BIZ-52 post-review optimizations

pool_manager.py

@@ -1,5 +1,6 @@
 """Provider pool management: primary / fallback pool routing."""
 
+import random
 import structlog
 from typing import Optional
 
@@ -42,6 +43,7 @@ class PoolManager:
             if pool:
                 break
 
+        random.shuffle(backends)
         return backends
 
     def get_any_healthy_backends(self, pool: Optional[str] = None) -> list[Backend]:
@@ -55,6 +57,7 @@ class PoolManager:
                     backends.append(b)
             if pool:
                 break
+        random.shuffle(backends)
         return backends
 
     def get_pool_status(self) -> dict: