docs(agents): fix broken agent snippets and stale API claims

[GWeale]

Corrections to the core agent pages (docs/agents/): snippets that don't run as written, plus behavioral claims that no longer match Python v2.5.0.

Changes

• docs/agents/llm-agents.md — create_session() was shown as a plain synchronous call; it's async, so the example now wraps it in asyncio.run(...). Two planner examples omitted the required name on Agent(...). An instruction example embedded {country}, which ADK treats as a state-injection placeholder, so it's now a literal country. Also: model is optional in Python (inherits from the nearest ancestor, else the built-in default), global_instruction is deprecated in favor of GlobalInstructionPlugin, input_schema applies when the agent is invoked as a tool rather than to direct user messages, generate_content_config raises ValueError if it sets tools/system_instruction/response_schema, and output_schema is no longer described as incompatible with tools.
• docs/agents/custom-agents.md — the "agent as a tool" snippet used Event and types without importing them, and called types.Part.from_bytes positionally when its arguments are keyword-only; both fixed. Adds that BaseAgent is a Pydantic model with extra='forbid', so sub-agents must be declared as annotated fields rather than assigned in __init__, and that live runs need _run_live_impl or raise NotImplementedError.
• docs/agents/workflow-agents/index.md, sequential-agents.md, parallel-agents.md, loop-agents.md — SequentialAgent, ParallelAgent and LoopAgent now emit a DeprecationWarning on construction; each page says so. Fixes a broken ##data-handling anchor (double #).
• docs/agents/workflow-agents/loop-agents.md — max_iterations was implied to be set by default; it defaults to None, so the loop only stops on escalation. Termination was described vaguely ("return a STOP signal"); it's now the concrete mechanism — an event with actions=EventActions(escalate=True), ctx.actions.escalate, or the built-in exit_loop tool.
• docs/agents/workflow-agents/parallel-agents.md — said there is no state sharing between branches. Only conversation history is branch-local; session state is shared, so the "pass a shared InvocationContext and use locks" advice is replaced with output_key plus a warning not to read a key another branch is still writing.
• docs/agents/managed-agents.md — the persisted event value is interaction_id, not previous_interaction_id, and it's sent back to the backend rather than reused locally. "MCP tools are not supported" was too broad: raw types.Tool.mcp_servers configs raise NotImplementedError, but server-side RemoteMcpServer specs work. Adds mode='single_turn' and the newer samples.
• docs/agents/config.md — "only Gemini models are supported" applied to the whole feature; the restriction is on the model: key. Other models go through model_code:, and the two keys are mutually exclusive.

How this was produced

Part of a page-by-page audit of the Python docs against the google/adk-python v2.5.0 source: every import resolved against a real 2.5.0 install, every constructor kwarg checked against model_fields / inspect.signature, every documented default read off the field. A second independent pass re-derived each claim from source rather than trusting the finding, and a third conformed the new wording to the surrounding pages. mkdocs build --strict is clean.

Only Python tabs and language-neutral prose were touched — this audit had no ground truth for the Go / Java / TypeScript SDKs.

Split out of a larger audit branch so each area can be reviewed on its own.

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