fix: serialize empty MCP tool properties as {} not null for OpenAI - #28380

Summary

Fixed a bug where MCP tools with an empty properties schema had their tool definitions sent to OpenAI with "properties": null, causing OpenAI to reject the request.

Problem

When an MCP server reports a tool with an empty input schema, e.g.:

{
  "type": "object",
  "properties": {},
  "required": []
}

Coder was forwarding the tool definition to OpenAI as:

{
  "type": "object",
  "properties": null
}

OpenAI's function-calling API rejects properties: null, making these tools unusable with OpenAI models.

Root cause

The empty properties object collapsed to Go nil at two layers:

1. agent/x/agentmcp/manager.go toolInputSchemaMap stripped the present-but-empty "properties": {} (guarded by len(properties) > 0), so the wire copy lost it entirely.
2. coderd/x/chatd/chatloop/chatloop.go buildToolDefinitions embedded info.Parameters directly into the input schema. When nil, encoding/json marshals it as null.

Fix

• buildToolDefinitions now substitutes an empty object when Parameters is nil, mirroring the existing required guard (the sink, protects all tool sources).
• toolInputSchemaMap now preserves an empty properties object instead of dropping it (the upstream producer).

Tests

Added regression tests (failing before, passing after) covering both layers and asserting the schema serializes to {"type":"object","properties":{}}:

• TestBuildToolDefinitionsNilPropertiesBecomesEmptyObject
• TestToolInputSchemaMapPreservesEmptyProperties
• TestWorkspaceMCPToolInfosFromResources/EmptyPropertiesYieldsEmptySchema

This PR was generated by Coder Agents.