[Feature]: Add Cursor SDK support to the Cursor provider

[laxman-patel]

Before submitting

• I searched existing issues and did not find a duplicate.
• I am describing a concrete problem or use case, not just a vague idea.

Area

apps/server

Problem or use case

Cursor recently launched the Cursor SDK (currently in beta). Today the Cursor provider in t3code only talks to cursor-agent over ACP, so we can't use the SDK...

Proposed solution

Add a Cursor SDK runtime mode alongside ACP. Per-instance toggle in settings. SDK handles model discovery, streaming, and tool-call events directly. ACP stays as the other option.

Why this matters

Cursor users get access to the new SDK surface, Composer models, partial tool calls, shell output in the right card, limit resets, thinking/token telemetry, without waiting for the CLI to catch up. ACP users aren't forced to switch.

Smallest useful scope

One Cursor instance in SDK mode with model discovery, assistant text + tool call streaming, and the settings toggle. Rest is polish.

Alternatives considered

No response

Risks or tradeoffs

SDK is still in beta, so its event shape will shift; the event map needs defensive parsing and will need follow-ups. Two runtimes to maintain. Shell output is associated to the last started tool call, fine while Cursor runs tools serially. Auth differs between modes, so switching may require re-auth.

Examples or references

@cursor/sdk (official, beta)
pi-cursor-sdk - https://pi.dev/packages/pi-cursor-sdk?name=cursor

Here's my fork with a working Cursor SDK implementation, tested end-to-end: https://github.com/laxman-patel/t3code

Contribution

• I would be open to helping implement this.