feat: add Google/GitHub social login for Demo environment (GRO-531)

- auth.ts: add google/github social providers from better-auth/social-providers
- auth.ts: add getActiveProviders() to enumerate configured OAuth/social providers
- index.ts: add /api/auth/providers public endpoint for frontend
- App.tsx: update LoginPage to show Google/GitHub buttons based on /api/auth/providers response

Co-Authored-By: Paperclip <noreply@paperclip.ing>

apps/api/src/index.ts

@@ -2,7 +2,7 @@ import { serve } from "@hono/node-server";
 import { Hono } from "hono";
 import { logger } from "hono/logger";
 import { cors } from "hono/cors";
-import { getAuth, initAuth } from "./lib/auth.js";
+import { getAuth, initAuth, getActiveProviders } from "./lib/auth.js";
 import { clientsRouter } from "./routes/clients.js";
 import { petsRouter } from "./routes/pets.js";
 import { servicesRouter } from "./routes/services.js";
@@ -92,6 +92,11 @@ app.get("/api/setup/status", async (c) => {
   return c.json({ needsSetup: !superUser });
 });
 
+// Public auth providers endpoint — no auth required, tells frontend which login options are available
+app.get("/api/auth/providers", async (c) => {
+  return c.json({ providers: getActiveProviders() });
+});
+
 // Protected API routes
 const api = app.basePath("/api");
 api.use("*", authMiddleware);