In ADK 1.19.0 - I have observed:

Gemini Native ADK:

• Uses [role='system'] directly in [Content] objects
  OR passes [system_instruction] in [GenerateContentConfig] (not as a message)
• Gemini API natively understands this field

LiteLLM ADK Wrapper:

• Converts [system_instruction] to a message with [role='developer']
• Tries to use OpenAI's convention
• But the "developer" role is OpenAI-specific!
• Claude/Anthropic expect [role='system']
• LiteLLM's Anthropic handler filters for [role='system'], not [role='developer']

Result and bug: System instruction is ignored or mishandled.
This causes system instructions to be lost for Claude, resulting in a poorly formatted output.

The best is to patch ADK to use [role="system"] and that would work for everyone.
Here is a proposed patch.

# in lite_llm.py around like 902
messages.insert(
    0,
    ChatCompletionSystemMessage(  # Changed from ChatCompletionDeveloperMessage
        role="system",  # Changed from "developer"
        content=llm_request.config.system_instruction,
    ),
)