System prompt handling in Gemini

Question

I'm using the deprecated `google-generativeai` package (model: `gemini-2.0-flash`) and initialize the model as follows:
import google.generativeai as genai
genai.configure(api_key='GOOGLE_API_KEY')
model = genai.GenerativeModel(
    model_name='gemini-2.0-flash',
    system_instruction=system_instruction,
    generation_config=genai.GenerationConfig(temperature=0)
)
def generate_response(user_prompt):
    response = model.generate_content(user_prompt)
    return response
Questions about google-generativeai:
1. Is `system_instruction` sent with every request when calling the model.generate_content function?
2. Does Gemini cache `system_instruction` by default?
---
In the new `google-genai` package, the model is used like this:
from google import genai
from google.genai import types
client = genai.Client(api_key="GEMINI_API_KEY")
def generate_response(user_prompt):
    response = client.models.generate_content(
        model="gemini-2.0-flash",
        config=types.GenerateContentConfig(
            system_instruction="You are a cat. Your name is Neko."
        ),
        contents=user_prompt
    )
    return response
Questions about google-genai:
3. The `system_instruction` is passed with every request. Is there a way to set it once, like the deprecated version (google-generativeai)?
4. If not, how can I implement caching for `system_instruction` in the new package (google-genai)?