[API] Add error code field to the non-streaming chat errors

[roma-glushko]

Let's add

• the error code field to the non-streaming error messages to make that schema consistent with the streaming errors
• don't return 500 in case of no healthy model is in the router pool. Return 503 instead
• Separate the expected failure case (e.g. no model is available) from unexpected internal errors (e.g. nil pointer exceptions)
• make sure all response fields are consistently returned in camelCase