docs: improve Go library developer experience

[skyoo2003]

Description

Improve ACOR product experience for Go library users without changing the public API. The README and Quick Start now use context-first construction and operations, the API reference explains operation selection and typed error handling, and the existing examples demonstrate production-oriented context usage.

Type of Change

• Bug fix (non-breaking change which fixes an issue)
• New feature (non-breaking change which adds functionality)
• Breaking change (fix or feature that would cause existing functionality to not work as expected)
• Documentation update
• Refactoring (no functional changes)
• Test update

Checklist

• Tests pass (make test)
• Vet/make vet
• Linting passes (make lint)
• Build succeeds (make build)
• Documentation updated if needed
• Changelog fragment added (not included because this PR changes documentation and examples only; no runtime or release behavior)
• Commit messages follow guidelines

Additional Notes

• Verification also included doccheck for 22 Markdown Go blocks, builds for all three examples, and API snapshot verification with no public API diff.
• The local shell had a stale GOROOT pointing to Go 1.26.7 while the active tool was Go 1.27.1, so verification commands unset GOROOT for a consistent toolchain.
• The approved design and implementation plan remain excluded from commits and this PR.