docs: modernize README with clean hero, client badges, and native mermaid architecture

[engkinandatama]

Visual & Architectural Enhancement for README

Changes

• Enlarged Logo: Image width adjusted to 380px with redundant # BioContext text removed (logo already contains the typography).
• Refined Badges:
  • Removed personal ORCID from top badges (retained in academic citation metadata).
  • Added dedicated AI client support badges: Cursor, Claude Desktop & Code, Antigravity IDE, and Goose.
  • Retained PyPI, Zenodo DOI, Python versions, CI/CD, License, and MCP 2.x badges.
• Native Mermaid Architecture:
  • Replaced monospace ASCII box diagram with clean, responsive GitHub-native Mermaid graph with colored subsystem nodes.
  • Renders perfectly on both light and dark GitHub themes without font misalignment or breaking in PyPI.