Live API (gemini-3.1-flash-live-preview): model composes a function call in thinking but never emits it, speaks fabricated data instead

### Description

Using the Live API (bidi streaming / WebSocket) with `gemini-3.1-flash-live-preview`, `thinking_config` enabled (`thinking_level="low"`, `include_thoughts=True`), and function calling (a handful of tools registered), we intermittently observe the model:

1. Deciding to call a specific function and composing its exact arguments — visible verbatim in the returned `thought` parts (e.g. "I'll be using the `check_availability` tool to find the exact time slot... I'm ready to use the tools to finalize the appointment.")
2. **Never emitting the function call at all**, and instead speaking synthesized/fabricated data in the same turn as if a tool had already returned a result — with no disclaimer, no error, nothing to indicate the data wasn't real.

### Why we're confident this isn't a client-side/SDK issue

We captured every raw Live API server message before any client-side (ADK) processing — i.e. logging directly at the point our client library receives each message off the wire, before any filtering, dispatch, or turn-taking logic runs. Grepping the full raw capture for an affected call (6,000+ raw messages) for a non-null `tool_call`/`functionCall` field returns **zero matches for the entire call**, including every message in the turn where the model spoke the fabricated data. The function call structure was never present on the wire — not dropped by a client bug, not filtered, never sent by the server.

We also found the model's own thought text, ~2 seconds *after* it had already spoken the fabricated/ungrounded claim, saying (paraphrased) "my next step is to call [the tool]" — i.e. it appears to plan the tool call chronologically *after* already having spoken the content that call should have grounded. This looks like a turn-ordering/sequencing issue in generation, not a transport loss.

### Reproduction rate

Roughly 20-35% in our test conditions (multi-turn conversations that include at least one tool-calling decision, thinking enabled). We have not isolated the exact trigger — it reproduces on both simple single-tool turns and multi-turn conversations, doesn't correlate with any argument value we've been able to identify, and reproduces with both audio and text-simulated caller input.

### Related prior art

- https://discuss.ai.google.dev/t/gemini-2-5-flash-native-audio-dialog-live-multimodal-api-tool-calling/86467 — same symptom shape (model says "I'll do this" in audio, never calls the function) reported against `gemini-2.5-flash` native-audio in 2025; acknowledged by Google and improved in a later preview build for that model generation. We haven't found an equivalent report against `3.1-flash-live-preview`.
- #1894 and #843 in this repo — related but not identical: those describe the model speaking speculatively *around* a tool call that IS emitted, or "function calling not working" without the same composed-thought evidence we have here.

### Ask

Is this a known/expected failure mode for native-audio Live + function calling on this model version? We have detailed captured-thinking + raw-wire evidence (composed args in thought, zero wire-level function call, self-corrective thought after the fact) that's more specific than what we found in existing reports, and are happy to share a redacted reproduction script or full raw capture excerpt if useful for triage.

### Environment
- google-genai 2.10.0, google-adk 2.5.0 (ADK's Live client wraps this library; confirmed via raw wire capture that ADK is not involved in the drop)
- Model: gemini-3.1-flash-live-preview
- thinking_config: thinking_level="low", include_thoughts=True