feat: create a new canvas by copying an existing one

Add a 'Copy from existing' option to the New Canvas modal. It lists every
canvas with node/group/text counts; picking one deep-copies its nodes, edges,
parent/child links and canvas state (viewport, custom style, floor plan) into
a fresh design.

Backend: POST /designs/{source_id}/copy remaps node ids, re-points edges and
parent links, and clones canvas state; GET /designs now returns per-design
counts for the picker. Standalone mode clones the localStorage canvas.

Closes #216

ha-relevant: maybe

backend/app/schemas/designs.py

@@ -16,6 +16,13 @@ class DesignUpdate(BaseModel):
     icon: str | None = None
 
 
+class DesignCopy(BaseModel):
+    """Create a new design by deep-copying an existing one's canvas."""
+
+    name: str
+    icon: str = "dashboard"
+
+
 class DesignResponse(BaseModel):
     id: str
     name: str
@@ -23,5 +30,10 @@ class DesignResponse(BaseModel):
     icon: str | None = None
     created_at: datetime
     updated_at: datetime
+    # Populated by list_designs so the "copy from existing" picker can show what
+    # each canvas holds. None on create/update/copy responses (not computed there).
+    node_count: int | None = None
+    group_count: int | None = None
+    text_count: int | None = None
 
     model_config = {"from_attributes": True}