docs: update custom log handler example

[Galileo927]

Fixes #3763

Changes

Updates the Getting Started custom log handler example to register the handler using opentelemetry::nostd::shared_ptr<LogHandler>, matching the current GlobalLogHandler::SetLogHandler API.

The previous documentation used std::make_shared<CustomLogHandler>(), which does not match the exact API type when nostd::shared_ptr is not an alias to std::shared_ptr.

This change also makes the documentation consistent with the SDK test pattern in sdk/test/common/global_log_handle_test.cc.

This is a documentation-only change, so no changelog entry, unit test, or public API review is required.

Please provide a brief description of the changes here.

Testing

• Ran git diff --check
• Searched SetLogHandler, CustomLogHandler, and GlobalLogHandler usages
• Compiled the revised snippet with c++ -std=c++11 -Iapi/include -Isdk/include

For significant contributions please make sure you have completed the following items:

• CHANGELOG.md updated for non-trivial changes
• Unit tests have been added
• Changes in public API reviewed

[linux-foundation-easycla]

The committers listed above are authorized under a signed CLA.

• ✅ login: Galileo927 / name: Galileo927 (e3cb801)

[Copilot]

Pull request overview

This PR updates the Getting Started SDK documentation so the custom internal log handler example matches the current GlobalLogHandler::SetLogHandler API.

Changes:

• Adds guidance to register custom log handlers as opentelemetry::nostd::shared_ptr.
• Updates the example to construct a nostd::shared_ptr<LogHandler> before calling SetLogHandler.

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
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Additional details and impacted files

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