fix(client): fall back on legacy JSON-RPC errors

[j45856021-dev]

Summary

• Fall back from server/discover to legacy initialize for JSON-RPC errors that do not positively identify a modern server.
• Keep authentication, transport, lifecycle configuration, and recognized modern-protocol errors actionable instead of downgrading them.
• Add a regression test for the deployed -32000 unsupported MCP-Protocol-Version response, plus guards for modern capability and header errors.
• Clarify ClientLifecycleMode::Auto behavior in the README.

This addresses the JSON-RPC interoperability cases in #1040 and is a narrower alternative to #1133 after the review concern that Err(_) also catches 401/403 and client-side failures.

Motivation and Context

The 2026-07-28 compatibility guidance says a client should fall back when a legacy server returns an error that is not a recognized modern JSON-RPC error. Some deployed legacy servers reject the modern protocol header before dispatch with an implementation-defined response such as:

-32000 Bad Request: The MCP-Protocol-Version header value 2026-07-28 is not supported.

Current Auto handling only falls back for METHOD_NOT_FOUND, so these servers fail even though the configured legacy protocol works. This change limits the broader fallback to JsonRpcError; transport and authorization failures still surface unchanged.

How Has This Been Tested?

• cargo fmt --all --check
• cargo test -p rmcp --test test_client_lifecycle_modes --features client
• cargo test -p rmcp --test test_discover_http_client_startup --features client,reqwest,transport-streamable-http-client-reqwest,transport-streamable-http-server
• cargo clippy -p rmcp --test test_client_lifecycle_modes --features client -- -D warnings

Breaking Changes

None.

Types of changes

• Bug fix (non-breaking change which fixes an issue)
• New feature (non-breaking change which adds functionality)
• 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 style guidelines
• New and existing tests pass locally
• I have added appropriate error handling
• I have added or updated documentation as needed