fix: use getter for rootAgent to match Python SDK behavior

[mlingner]

Summary

Attempts to fix #82

I ran into this issue while building a TypeScript version of the weather bot tutorial. When a sub-agent completes and the model tries to return control to the root agent, it fails because the sub-agent's rootAgent property points to itself rather than the actual root.

Thanks to @santosflores for investigating this in #83, and to @ScottMansfield for pointing out that the Python SDK doesn't need recursive updates. It uses a computed property that walks up the parent chain each time.

This PR takes that same approach: replacing the cached rootAgent property with a getter, matching how the Python SDK handles it:

@property
def root_agent(self) -> BaseAgent:
    root_agent = self
    while root_agent.parent_agent is not None:
        root_agent = root_agent.parent_agent
    return root_agent

Changes

• Removed readonly rootAgent: BaseAgent property assignment in constructor
• Added get rootAgent(): BaseAgent getter that computes the root by walking up the parent chain

Reproduction

Minimal example:

import { FunctionTool, LlmAgent } from '@google/adk';
import { z } from 'zod';

const tellJoke = new FunctionTool({
    name: 'tell_joke',
    description: 'Tells a joke',
    parameters: z.object({}),
    execute: () => ({ joke: 'Why do programmers prefer dark mode? Because light attracts bugs!' }),
});

const subAgent = new LlmAgent({
    name: 'sub_agent',
    model: 'gemini-2.0-flash',
    description: 'Handles greetings',
    instruction: 'Greet the user.',
});

export const rootAgent = new LlmAgent({
    name: 'root_agent',
    model: 'gemini-2.0-flash',
    description: 'Main agent',
    instruction: 'Delegate greetings to sub_agent. For joke requests, use the tell_joke tool.',
    tools: [tellJoke],
    subAgents: [subAgent]
});

subAgent is created first, so its constructor sets rootAgent = this (pointing to itself). When it's later added to rootAgent via subAgents, the cached value is never updated.

Before fix:

[user]: hi
[sub_agent]: Hello!
[user]: tell me a joke
Error: Agent root_agent not found in the agent tree.

After fix:

[user]: hi
[sub_agent]: Hello!
[user]: tell me a joke
[root_agent]: Why do programmers prefer dark mode? Because light attracts bugs!

Test Plan

• Run unit tests in core/test/agents/base_agent_test.ts to verify sub-agents correctly resolve their rootAgent
• Test locally using the repro steps above

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[kalenkevich]

Thanks!

[santosflores]

Thanks a lot. I think solving this bug will result on the adk webserver in TS to finally display data inside the Trace tab. I'll try it once you release.

Attaching an image of the current behavior.

[mlingner]

Squashed into a single commit and fixed Prettier formatting in the test file for CI. :)