[Bug] RemoteTrigger.list: API returns next_cursor but tool wrapper exposes no cursor input parameter (pagination unusable from CLI)

Summary

The Claude Code RemoteTrigger tool wrapper's list action returns a next_cursor field in the response, but the tool schema exposes no input parameter to send that cursor back. As a result, accounts with more than ~20 triggers cannot enumerate beyond page 1 via the CLI tool, even though the API itself supports pagination.

The GUI / web Routines page does NOT have this limitation — all triggers are visible there. The fix appears to be partial: API server-side ready, GUI updated, CLI tool wrapper not yet updated.

Reproduce

From any Claude Code session in an account with >20 scheduled triggers:

RemoteTrigger { action: "list" }

Response structure (relevant parts):

{
  "data": [ /* 20 triggers */ ],
  "has_more": true,
  "next_cursor": "MTc3N...<base64 token>...="
}

Attempt to paginate:

RemoteTrigger { action: "list", body: { "cursor": "<token from next_cursor>" } }

Observed: identical page-1 response (verified by byte-identical content length and same first trigger ID).

RemoteTrigger { action: "list", body: { "next_cursor": "<token>" } }

Observed: also identical page-1 response. Body is silently dropped for the list action.

Tool schema (current)

{
  "action": { "enum": ["list", "get", "create", "update", "run"] },
  "body":   { /* required for create/update; optional for run */ },
  "trigger_id": { "pattern": "^[\\w-]+$" }
}

No top-level cursor parameter. Body is described as for write operations.

Expected

Either:

1. Add cursor as a top-level parameter on the tool, forwarded as a ?cursor=<token> query param to GET /v1/code/triggers.
2. Document that body for list accepts {cursor: "..."} and have the wrapper forward it accordingly.
3. Auto-paginate inside the wrapper and concatenate pages until has_more: false.

Any of the three resolves the gap.

Workaround

Maintain a local registry of trigger IDs out of band (markdown file, JSON, etc.). Use action: get with known IDs for individual fetches. Defeats the purpose of having a list endpoint, but works.

Environment

• Claude Code CLI v2.1.132
• Windows
• Account with 23 known scheduled triggers across multiple bot configurations; only 20 visible via the CLI tool wrapper, all 23 visible in the GUI Routines page.

Why this matters

Multi-bot / multi-trigger accounts cannot programmatically audit or manage their full trigger inventory from a Claude Code session. The fix appears small (the API plumbing is already done) but the gap blocks legitimate automation workflows.

Related (different problems, listed for context)

• #43440 RemoteTrigger / Scheduled Tasks API returns 500
• #44932 Remote Triggers: add execution history and run status
• #51854 Encrypted secrets store for scheduled triggers
• None found specifically addressing the pagination cursor gap.

Meta-pattern (constructive feedback)

This bug reflects a pattern where Anthropic ships GUI-side fixes faster than CLI-tool-wrapper fixes. A "tool wrapper parity" checklist for API changes might prevent the next instance.