feat(telemetry): capture tool execution error code in OpenTelemetry spans

[Achuth17]

Introduces ToolExecutionError and ToolErrorType (HTTP status codes) to standardize error reporting for tool failures. Updates trace_tool_call and function execution handlers to extract and record error.type semantics.

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Link to Issue or Description of Change

1. Link to an existing issue (if applicable):

• Closes: Support Error Codes in Traces sent during Tool Call Failures #4614

2. Or, if no issue exists, describe the change:

If applicable, please follow the issue templates to provide as much detail as
possible.

Problem:
A clear and concise description of what the problem is.

Solution:
A clear and concise description of what you want to happen and why you choose
this solution.

Testing Plan

• Added tests for different supported error code scenarios (InternalServerError, Timeout) and an unsupported error code scenario (ValueError) where the error.code falls back to the error's class name.

Unit Tests:

• I have added or updated unit tests for my change.
• All unit tests pass locally.

Please include a summary of passed pytest results.

Manual End-to-End (E2E) Tests:

• Tested manually using adk web

Checklist

• I have read the CONTRIBUTING.md document.
• I have performed a self-review of my own code.
• I have commented my code, particularly in hard-to-understand areas.
• I have added tests that prove my fix is effective or that my feature works.
• New and existing unit tests pass locally with my changes.
• I have manually tested my changes end-to-end.
• Any dependent changes have been merged and published in downstream modules.

Additional context

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[ryanaiagent]

Hi @Achuth17 , Thank you for your contribution through this pull request! This PR has merge conflicts that require changes from your end. Could you please rebase your branch with the latest main branch to address these? Once this is complete, please let us know so we can proceed with the review.

[Achuth17]

Merge conflicts should be fixed now, please take a look.

[Achuth17]

@ryanaiagent Is this an automated closure?

Why does extending the telemetry of ADK belong in the adk-docs/integrations repo?

[ryanaiagent]

Hi @Achuth17 , please fix the failing mypy-diff tests, unit tests and fix formatting errors by running autoformat.sh.