fix(tools): normalize truly empty MCP tool schemas for OpenAI

Fixes #60158

MCP tools with parameter-free schemas may return truly empty objects
`{}` without a `type` field. The existing normalization handled
`{ type: "object" }` → `{ type: "object", properties: {} }` but
missed the truly empty case.

OpenAI gpt-5.4 rejects tool schemas without `type: "object"` and
`properties`, causing HTTP 400 errors:

```
Invalid schema for function 'flux-mcp__get_flux_instance':
In context=(), object schema missing properties.
```

This change catches empty schemas (no type, no properties, no unions)
before the final pass-through and converts them to the required format.

Added test case for parameter-free MCP tool schemas.

src/agents/pi-tools.schema.test.ts

@@ -4,6 +4,22 @@ import { normalizeToolParameters } from "./pi-tools.schema.js";
 import type { AnyAgentTool } from "./pi-tools.types.js";
 
 describe("normalizeToolParameters", () => {
+  it("normalizes truly empty schemas to type:object with properties:{} (MCP parameter-free tools)", () => {
+    const tool: AnyAgentTool = {
+      name: "get_flux_instance",
+      label: "get_flux_instance",
+      description: "Get current Flux instance status",
+      parameters: {},
+      execute: vi.fn(),
+    };
+
+    const normalized = normalizeToolParameters(tool);
+
+    const parameters = normalized.parameters as Record<string, unknown>;
+    expect(parameters.type).toBe("object");
+    expect(parameters.properties).toEqual({});
+  });
+
   it("injects properties:{} for type:object schemas missing properties (MCP no-param tools)", () => {
     const tool: AnyAgentTool = {
       name: "list_regions",

src/agents/pi-tools.schema.ts

@@ -133,6 +133,12 @@ export function normalizeToolParameterSchema(
       ? "oneOf"
       : null;
   if (!variantKey) {
+    // Handle truly empty schemas (no type, no properties, no unions) —
+    // OpenAI requires `type: "object"` with `properties` for tool schemas.
+    // MCP tools with parameter-free schemas may return `{}` or minimal objects.
+    if (!("type" in schemaRecord) && !("properties" in schemaRecord)) {
+      return applyProviderCleaning({ type: "object", properties: {}, ...schemaRecord });
+    }
     return schema;
   }
   const variants = schemaRecord[variantKey] as unknown[];