refactor: remove request_ctx ContextVar, thread Context explicitly

[maxisbey]

Removes the request_ctx ContextVar and threads Context explicitly through the MCPServer request-handling chain.

Motivation and Context

The request_ctx ContextVar in mcp.server.lowlevel.server was redundant: the lowlevel server already passes ServerRequestContext as the first argument to every _handle_* method. The ContextVar was a second mechanism carrying the same value, used only by MCPServer.get_context().

This PR removes the ContextVar entirely, making the data flow explicit. _handle_* methods construct the high-level Context at the lowlevel→MCPServer boundary and pass it through.

Part of #2112 (context refactor) / #1684 (contextvars cleanup).

How Has This Been Tested?

• All existing tests pass (1123 passed, 98 skipped, 1 xfailed)
• New tests for the context-required guards in Tool.run(), Prompt.render(), ResourceTemplate.create_resource()
• uv run --frozen pyright src/ tests/ — 0 errors
• uv run --frozen ruff check — clean

Breaking Changes

Yes — documented in docs/migration.md:

• MCPServer.get_context() removed — use ctx: Context parameter injection in tool/resource/prompt functions instead (the existing recommended pattern)
• request_ctx ContextVar removed from mcp.server.lowlevel.server — code importing it directly will need to use parameter injection
• MCPServer.call_tool(), read_resource(), get_prompt() now accept an optional context: Context | None = None parameter — backward-compatible for callers that don't pass it
• New behavior: if a tool/resource/prompt declares a ctx: Context parameter but is called with context=None, a clear error is raised (ToolError for tools, ValueError for prompts/resource templates). Previously None was silently injected.

Types of changes

• Breaking change (fix or feature that would cause existing functionality to change)
• Documentation update

Checklist

• I have read the MCP Documentation
• My code follows the repository's style guidelines
• New and existing tests pass locally
• I have added appropriate error handling
• I have added or updated documentation as needed

Additional context

Context class moved from mcp.server.mcpserver.server to mcp.server.mcpserver.context. The public import path (from mcp.server.mcpserver import Context) is unchanged via __init__.py re-export. The old direct-module path (from mcp.server.mcpserver.server import Context) also still works because server.py imports Context at module level.

Exception hierarchy cleanup (making prompts/resources raise MCPServerError subclasses instead of ValueError) was considered but deferred to #1742 (error taxonomy) to avoid scope creep — see that issue for the full analysis of the existing inconsistencies.

_{AI Disclaimer}