docs: restructure README into docs/ pages

Move detailed feature documentation from README.md into organized docs/ files.
README becomes a thin entry point (187 lines) with project description, install,
quickstart, and links to docs/.

New files (content moved from README):
- docs/server.md: tools, resources, prompts, structured output, icons, images,
  context, completions, elicitation, sampling, logging, transports, ASGI mounting,
  pagination, FastMCP/session/request-context properties
- docs/client.md: writing MCP clients (stdio + HTTP), display utilities,
  parsing tool results
- docs/protocol.md: MCP primitives table, server capabilities table

Sections replaced with links to existing docs:
- Authentication -> docs/authorization.md
- Low-Level Server -> docs/low-level-server.md

No new content added — pure reorganization.

Author: felixweinberger