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.:

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

Coder was forwarding the tool definition to OpenAI as:

```json
{
  "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.*

coderd/x/chatd/chatloop/chatloop.go

@@ -1628,9 +1628,16 @@ func buildToolDefinitions(tools []fantasy.AgentTool, activeTools []string, provi
 			continue
 		}
 
+		// Substitute an empty object for nil properties so that a tool
+		// with no parameters never serializes "properties" to null,
+		// which OpenAI rejects.
+		properties := info.Parameters
+		if properties == nil {
+			properties = map[string]any{}
+		}
 		inputSchema := map[string]any{
 			"type":       "object",
-			"properties": info.Parameters,
+			"properties": properties,
 		}
 		// Only include "required" when non-empty so that a nil slice
 		// never serializes to null, which OpenAI rejects.

coderd/x/chatd/chatloop/chatloop_internal_test.go

@@ -2,6 +2,7 @@ package chatloop
 
 import (
 	"context"
+	"encoding/json"
 	"iter"
 	"testing"
 
@@ -81,6 +82,52 @@ func TestProcessStepStreamPersistsRedactedThinkingOnEnd(t *testing.T) {
 	require.Equal(t, "redacted-payload", metadata.RedactedData)
 }
 
+// staticParametersTool returns a fixed ToolInfo, letting a test control
+// Parameters directly. fantasy.NewAgentTool always generates a non-nil
+// Parameters map, so it cannot reproduce the nil Parameters that MCP tool
+// wrappers report for a schema with an empty "properties" object.
+type staticParametersTool struct {
+	fantasy.AgentTool
+	info fantasy.ToolInfo
+}
+
+func (t staticParametersTool) Info() fantasy.ToolInfo { return t.info }
+
+func (staticParametersTool) ProviderOptions() fantasy.ProviderOptions { return nil }
+
+// TestBuildToolDefinitionsNilPropertiesBecomesEmptyObject verifies that a
+// tool whose input schema has no properties (for example an MCP tool
+// reporting {"type": "object", "properties": {}}) still serializes
+// "properties" as an empty JSON object. A nil Parameters map would serialize
+// to null, which OpenAI rejects with "Invalid schema for function ... None is
+// not of type 'object'".
+func TestBuildToolDefinitionsNilPropertiesBecomesEmptyObject(t *testing.T) {
+	t.Parallel()
+
+	tool := staticParametersTool{
+		info: fantasy.ToolInfo{
+			Name:        "document_graphql_schema",
+			Description: "Run a GraphQL query",
+			Parameters:  nil,
+		},
+	}
+
+	defs := buildToolDefinitions([]fantasy.AgentTool{tool}, nil, nil)
+	require.Len(t, defs, 1)
+
+	ft, ok := defs[0].(fantasy.FunctionTool)
+	require.True(t, ok, "expected a fantasy.FunctionTool")
+
+	properties, ok := ft.InputSchema["properties"].(map[string]any)
+	require.True(t, ok, "properties must be a map, got %T", ft.InputSchema["properties"])
+	require.NotNil(t, properties, "properties must not be nil")
+
+	// Verify it serializes to {} not null.
+	bs, err := json.Marshal(ft.InputSchema)
+	require.NoError(t, err)
+	require.JSONEq(t, `{"type":"object","properties":{}}`, string(bs))
+}
+
 func TestFlushActiveStatePreservesEmptySignedReasoning(t *testing.T) {
 	t.Parallel()
 

coderd/x/chatd/context_prompt_internal_test.go

@@ -735,6 +735,31 @@ func TestWorkspaceMCPToolInfosFromResources(t *testing.T) {
 		require.Equal(t, "playwright__navigate", infos[0].Name)
 	})
 
+	t.Run("EmptyPropertiesYieldsEmptySchema", func(t *testing.T) {
+		t.Parallel()
+
+		// An MCP tool reporting {"type": "object", "properties": {}} must
+		// produce a non-nil empty Schema. A nil Schema serializes to JSON
+		// null downstream, which OpenAI rejects.
+		schema := mustStruct(t, map[string]any{
+			"type":       "object",
+			"properties": map[string]any{},
+		})
+		resources := []database.ChatContextResource{
+			mcpServerResource(t, "github", &agentproto.MCPServerBody{
+				ServerName: "github",
+				Tools: []*agentproto.MCPTool{
+					{Name: "document_graphql_schema", Description: "Run a GraphQL query", InputSchema: schema},
+				},
+			}, database.WorkspaceAgentContextResourceStatusOk),
+		}
+
+		infos := workspaceMCPToolInfosFromResources(resources)
+		require.Len(t, infos, 1)
+		require.NotNil(t, infos[0].Schema, "Schema must not be nil for an empty properties object")
+		require.Empty(t, infos[0].Schema)
+	})
+
 	t.Run("NoMCPServersYieldsNil", func(t *testing.T) {
 		t.Parallel()