Add client-level connect handshake to stdio transport

## Motivation and Context

This commit implements Phase 1 of 3 for #334.

The MCP specification requires an `initialize` request followed by
a `notifications/initialized` notification before any other interaction.
PR #327 added `MCP::Client#connect` and `MCP::Client::HTTP#connect`
to expose this handshake explicitly for the HTTP transport,
but stdio remained on its private `initialize_session` lazy-init path,
inconsistent with the Python SDK (`ClientSession.initialize()`) and
TypeScript SDK (`Client.connect(transport)`),
both of which require an explicit handshake call regardless of transport.

The implicit init path on the first `send_request` is
preserved as a non-breaking compatibility shim. Public API added on `Stdio`:

- `connect(client_info:, protocol_version:, capabilities:)` performs the
  handshake, validates the negotiated `protocolVersion` against
  `MCP::Configuration::SUPPORTED_STABLE_PROTOCOL_VERSIONS`,
  caches the `InitializeResult`, and is idempotent.
- `connected?` reports handshake completion.
- `server_info` exposes the cached `InitializeResult`.

Documentation and examples are updated so new users learn the explicit pattern
from the start.

## How Has This Been Tested?

Fifteen regression tests cover: explicit handshake, `server_info` caching,
idempotence, custom keyword arguments, JSON-RPC error response, missing
or non-Hash `result`, unsupported protocol version with state rollback,
state rollback when the `notifications/initialized` write fails,
retry after a failed handshake, and the `connected?` / `server_info` lifecycle.

The pre-existing stdio tests pass without modification, verifying that
the implicit-init compatibility path still works.

## Breaking Changes

None for the typical "implicit init via `client.tools` / `client.call_tool`" usage.
Existing stdio clients keep working unchanged.

Three observable behavior changes for code that inspects transport state directly:

- `Client#connected?` for a never-initialized stdio client returns `false`
  (previously fell through to a `true` default via the `respond_to?` fallback).
- `Client#server_info` for stdio returns the cached `InitializeResult`
  after the handshake (previously always `nil` via the fallback).
- The implicit handshake path now validates the server's negotiated
  protocol version, raising `RequestHandlerError` for unsupported versions.
  Production servers that return one of the supported versions are unaffected;
  this closes a pre-existing spec-conformance gap on stdio.

examples/README.md

@@ -28,10 +28,10 @@ $ ruby examples/stdio_client.rb
 
 The client will automatically launch `stdio_server.rb` as a subprocess and demonstrate:
 
+- Performing the MCP initialization handshake via `client.connect`
 - Listing and calling tools
 - Listing prompts
 - Listing and reading resources
-- Automatic MCP protocol initialization
 - Transport cleanup on exit
 
 ### 3. HTTP Server (`http_server.rb`)