feat(config-yaml): support configuring MCP server transport

[nejch]

Description

Adds support for transport type (enabling SSE use via YAML).

Closes #5359

Checklist

• I've read the contributing guide
• The relevant docs, if any, have been updated or created
• The relevant tests, if any, have been updated or created

[netlify]

✅ Deploy Preview for continuedev canceled.

Name	Link
🔨 Latest commit	c645517
🔍 Latest deploy log	https://app.netlify.com/sites/continuedev/deploys/681797e6535556000812dc33

[enzoescipy]

Hi @nejch, thank you for initiating this important feature to support SSE/WebSocket transports for MCP servers! We were also really looking forward to this capability for our own setup.
Since the PR is currently in draft and we were quite eager to use this feature, we took the liberty of building upon your work to see if we could get a version running quickly.
We've managed to get a working version (at least for our use case) implemented in our fork, which you can find here:
https://github.com/enzoescipy/continue/tree/sse-mcp-support
It mainly involved completing the URL handling in loadYaml.ts and ensuring the schema definition in schemas/index.ts was correct. The core connection logic in MCPConnection.ts was already mostly there!
Please feel free to use this as a reference, or even integrate parts of it if it helps you finalize your PR. No pressure at all, just wanted to share what we quickly put together in case it's useful! Thanks again for getting this started.

[nejch]

Thanks @enzoescipy for taking the time for this - I'll admit I just pushed a quick draft yesterday without properly going through it. It seems like #5517 is more complete so feel free to add your feedback there, I'll close this one 🙇