fix(bfl): correct mode and variable shadowing from review feedback

- Change mode from "image_generation" to "image_edit" for all 4 BFL
  image edit models (flux-kontext-pro, flux-kontext-max, flux-pro-1.0-fill,
  flux-pro-1.0-expand)
- Rename shadowed api_base variable to complete_url in async handler
  for consistency with sync path

litellm/llms/black_forest_labs/image_edit/handler.py

@@ -211,7 +211,6 @@ class BlackForestLabsImageEdit:
         if extra_headers:
             headers.update(extra_headers)
 
-        # Get complete URL
         # Get complete URL
         complete_url = self.config.get_complete_url(
             model=model,
@@ -236,7 +235,7 @@ class BlackForestLabsImageEdit:
             api_key="",
             additional_args={
                 "complete_input_dict": data,
-                "api_base": api_base,
+                "api_base": complete_url,
                 "headers": headers,
             },
         )
@@ -244,7 +243,7 @@ class BlackForestLabsImageEdit:
         # Make initial request
         try:
             response = await async_client.post(
-                url=api_base,
+                url=complete_url,
                 headers=headers,
                 json=data,
                 timeout=timeout,

model_prices_and_context_window.json

@@ -7788,7 +7788,7 @@
     },
     "black_forest_labs/flux-kontext-pro": {
         "litellm_provider": "black_forest_labs",
-        "mode": "image_generation",
+        "mode": "image_edit",
         "output_cost_per_image": 0.04,
         "source": "https://bfl.ai/pricing",
         "supported_endpoints": [
@@ -7797,7 +7797,7 @@
     },
     "black_forest_labs/flux-kontext-max": {
         "litellm_provider": "black_forest_labs",
-        "mode": "image_generation",
+        "mode": "image_edit",
         "output_cost_per_image": 0.08,
         "source": "https://bfl.ai/pricing",
         "supported_endpoints": [
@@ -7806,7 +7806,7 @@
     },
     "black_forest_labs/flux-pro-1.0-fill": {
         "litellm_provider": "black_forest_labs",
-        "mode": "image_generation",
+        "mode": "image_edit",
         "output_cost_per_image": 0.05,
         "source": "https://bfl.ai/pricing",
         "supported_endpoints": [
@@ -7815,7 +7815,7 @@
     },
     "black_forest_labs/flux-pro-1.0-expand": {
         "litellm_provider": "black_forest_labs",
-        "mode": "image_generation",
+        "mode": "image_edit",
         "output_cost_per_image": 0.05,
         "source": "https://bfl.ai/pricing",
         "supported_endpoints": [