feat(FN-5601): add OpenAI Responses API type support to custom providers

Added OpenAI Responses API as a new custom provider type, wiring `apiType: "responses"` through the core registry, engine routes, and dashboard UI with a dropdown selector; includes test coverage across the registry, routes, and component layers.

Fusion-Task-Id: FN-5601

Co-authored-by: Fusion (runfusion.ai) <noreply@runfusion.ai>
Fusion-Task-Id: FN-5601

packages/core/src/__tests__/custom-provider-key.test.ts

@@ -0,0 +1,50 @@
+import { describe, expect, it } from "vitest";
+import type { CustomProvider } from "../types.js";
+import { customProviderRegistryKey } from "../custom-provider-key.js";
+
+function provider(id: string, name: string): CustomProvider {
+  return {
+    id,
+    name,
+    apiType: "openai-compatible",
+    baseUrl: "https://example.test",
+  };
+}
+
+describe("customProviderRegistryKey", () => {
+  it("slugifies provider names", () => {
+    const providers = [provider("1", "My AI Provider")];
+    expect(customProviderRegistryKey(providers[0]!, providers)).toBe("my-ai-provider");
+  });
+
+  it("handles punctuation and non-ascii", () => {
+    const providers = [provider("1", "  Héllø!!! Provider ###  ")];
+    expect(customProviderRegistryKey(providers[0]!, providers)).toBe("h-ll-provider");
+  });
+
+  it("falls back to id when name slug is empty", () => {
+    const providers = [provider("550e8400-e29b-41d4-a716-446655440000", "!!!")];
+    expect(customProviderRegistryKey(providers[0]!, providers)).toBe("550e8400-e29b-41d4-a716-446655440000");
+  });
+
+  it("adds deterministic suffixes for two-way collisions", () => {
+    const providers = [provider("1", "A"), provider("2", "A")];
+    expect(customProviderRegistryKey(providers[0]!, providers)).toBe("a");
+    expect(customProviderRegistryKey(providers[1]!, providers)).toBe("a-2");
+  });
+
+  it("adds deterministic suffixes for three-way collisions", () => {
+    const providers = [provider("1", "A"), provider("2", "A"), provider("3", "A")];
+    expect(customProviderRegistryKey(providers[0]!, providers)).toBe("a");
+    expect(customProviderRegistryKey(providers[1]!, providers)).toBe("a-2");
+    expect(customProviderRegistryKey(providers[2]!, providers)).toBe("a-3");
+  });
+
+  it("is stable for the same ordered list", () => {
+    const providers = [provider("1", "A"), provider("2", "A")];
+    const first = customProviderRegistryKey(providers[1]!, providers);
+    const second = customProviderRegistryKey(providers[1]!, providers);
+    expect(first).toBe("a-2");
+    expect(second).toBe("a-2");
+  });
+});