Add Hamiltonian Energy optimization example

[caijintaoduolacmeng-star]

Summary

• Add an examples/ directory with a Hamiltonian Energy Quantum Function optimization script.
• Build the workload with typed ionq_core.models, submit via create_job, poll via wait_for_job, and parse the returned energy.
• Document setup, the example Hamiltonian/ansatz/backend, and both Unix and PowerShell API-key commands.

Closes #58

Verification

• ruff check examples README.md -> All checks passed
• ruff format --check examples -> 1 file already formatted
• ty check examples/ -> All checks passed
• git diff --check -> passed
• payload serialization sanity check -> passed