feat(client/sse): allow to set the timeout of POST /messages

[RockChinQ]

Motivation and Context

Hello. I'm writing a plugin for langgenius/dify that can export workflows on Dify as MCP Servers.
Due to Dify's plugin mechanism, connecting to Dify's cloud edition via HTTP takes a longer time. The GET /sse endpoint can set a timeout through the parameters of the sse_client method, while the POST /messages endpoint cannot, which results in the handshake phase not functioning properly.
So I reused the parameters read and sse_read_timeout of the sse_cient method as timeout settings for POST/messages.

How Has This Been Tested?

before: failed fast in 5s for timeout

after: ok for handshake phase (404 for /messages endpoint not fully implemented)

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'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

Although it works now, but I still wonder is this ok to just reuse the sse_read_timeout as timeout param for /messages endpoint, or should I add a new param like messages_read_timeout for sse_client()?

[RockChinQ]

Can anyone review or give some comment on this?

[Kludex]

The timeout needs to be set on the client above.