Update OpenAI-compatible auth docs

docs/integrations/openai-compatible-chat.md

@@ -122,7 +122,12 @@ Structured output is currently `json_schema` only, serialized as:
 
 ## Authentication Header
 
-If `Target.APIKeyEnv` is set:
+If `Target.APIKey` is set:
+
+- set `Authorization: Bearer <value>`
+- do not read `Target.APIKeyEnv`
+
+If `Target.APIKey` is empty and `Target.APIKeyEnv` is set:
 
 - resolve environment variable value at request time
 - set `Authorization: Bearer <value>`
@@ -131,7 +136,7 @@ If the environment variable is unset/empty:
 
 - request fails before HTTP call (`ErrInvalidRequest`)
 
-If `Target.APIKeyEnv` is empty:
+If both `Target.APIKey` and `Target.APIKeyEnv` are empty:
 
 - no `Authorization` header is sent