Make _live_api_client a public, documented override point (like api_client)

[smetanokr]

🔴 Required Information

Is your feature request related to a specific problem?

The Gemini class has a private _live_api_client property (leading underscore) that subclasses must override to customize the genai.Client used for Live API connections. This is contradictory — Python convention treats _-prefixed names as implementation details not intended for external override, yet Live API customization requires it.

The existing docstring documents how to override api_client for non-Live usage, but there's no public equivalent for Live API.

Describe the Solution You'd Like

Rename _live_api_client to live_api_client (remove leading underscore) and update the docstring to document the override pattern, similar to the existing api_client example:

class LiveGemini(Gemini):
    @cached_property
    def live_api_client(self):
        return genai.Client(enterprise=True, location="europe-central2")

Update the class docstring to include something like:

Customizing the underlying Live Client:
    To set ``google.genai.Client`` options for the Live API connection,
    subclass ``Gemini`` and override the ``live_api_client`` property::

        from functools import cached_property
        from google.adk.models import Gemini
        from google.genai import Client

        class LiveGemini(Gemini):
            @cached_property
            def live_api_client(self):
                return Client(enterprise=True, location="europe-central2")

Impact on your work

We deploy Gemini agents on Vertex AI in a specific region. Without overriding _live_api_client, all Live API connections default to us-central1. We had to discover this private property by reading source code — it's not discoverable from the public API.

Willingness to contribute

Yes, happy to submit a PR if the change direction is approved.

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🟡 Recommended Information

Describe Alternatives You've Considered

• Overriding api_client only: doesn't work, Live API uses _live_api_client, not api_client.
• Setting location via http_options on the model config: ADK doesn't expose a field for this on Live API connections.

Proposed API / Implementation

In google_llm.py:

1. Rename _live_api_client → live_api_client (both the @cached_property and its usage in connect()).
2. Add the docstring section shown above.
3. Keep _live_api_client as a deprecated alias pointing to live_api_client for backward compatibility.

Additional Context

The api_client property already follows this public-override pattern successfully. The _live_api_client property was introduced later (for the Live API code path) but its usage pattern is identical — subclasses need to override it — yet it was mistakenly made private.

[sanketpatil06]

Hi @smetanokr, thanks for reporting this. If you have a solution in mind, please feel free to raise a PR; our team will be happy to review it. We appreciate your contribution.