[Client] docs: introduce client SDK documentation and improve README structure (#259)

* docs: add comprehensive client SDK documentation

- Create new client documentation with examples and API reference
- Restructure README for better clarity and flow
- Add client examples to documentation index
- Update roadmap to mark client component as complete

* Update README.md

Co-authored-by: Christopher Hertel <mail@christopher-hertel.de>

* Apply suggestions from code review

Co-authored-by: Christopher Hertel <mail@christopher-hertel.de>

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Co-authored-by: Christopher Hertel <mail@christopher-hertel.de>

Author: CodeWithKyrian