Fix compatibility with region inference (#531)

* #508 Fix compatibility with region inference and resolve issues with different regions

* Reformat following  CI (#531)
* Two spaces before comment

backend/app/bedrock.py

@@ -259,18 +259,19 @@ def calculate_price(
 
 def get_model_id(model: type_model_name) -> str:
     # Ref: https://docs.aws.amazon.com/bedrock/latest/userguide/model-ids-arns.html
+    region = BEDROCK_REGION.split("-")[0]  # Cross-region inference
     if model == "claude-v2":
         return "anthropic.claude-v2:1"
     elif model == "claude-instant-v1":
         return "anthropic.claude-instant-v1"
     elif model == "claude-v3-sonnet":
-        return "anthropic.claude-3-sonnet-20240229-v1:0"
+        return f"{region}.anthropic.claude-3-sonnet-20240229-v1:0"
     elif model == "claude-v3-haiku":
-        return "anthropic.claude-3-haiku-20240307-v1:0"
+        return f"{region}.anthropic.claude-3-haiku-20240307-v1:0"
     elif model == "claude-v3-opus":
-        return "anthropic.claude-3-opus-20240229-v1:0"
+        return f"{region}.anthropic.claude-3-opus-20240229-v1:0"
     elif model == "claude-v3.5-sonnet":
-        return "anthropic.claude-3-5-sonnet-20240620-v1:0"
+        return f"{region}.anthropic.claude-3-5-sonnet-20240620-v1:0"
     elif model == "mistral-7b-instruct":
         return "mistral.mistral-7b-instruct-v0:2"
     elif model == "mixtral-8x7b-instruct":