test: add Playwright E2E test suite (30 tests)

Add browser-level end-to-end tests covering public pages, Keycloak
OAuth authentication flow, dashboard interactions, providers config,
developer section, organization pages, and sidebar navigation.

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

playwright.config.ts

@@ -0,0 +1,40 @@
+import { defineConfig, devices } from "@playwright/test";
+
+export default defineConfig({
+  testDir: "./e2e",
+  fullyParallel: true,
+  forbidOnly: !!process.env.CI,
+  retries: process.env.CI ? 2 : 0,
+  workers: process.env.CI ? 1 : undefined,
+  reporter: [["html"], ["list"]],
+  timeout: 30_000,
+
+  use: {
+    baseURL: process.env.BASE_URL ?? "http://localhost:8000",
+    actionTimeout: 10_000,
+    trace: "on-first-retry",
+    screenshot: "only-on-failure",
+  },
+
+  projects: [
+    {
+      name: "setup",
+      testMatch: /auth\.setup\.ts/,
+    },
+    {
+      name: "public",
+      testMatch: /public\.spec\.ts/,
+      use: { ...devices["Desktop Chrome"] },
+    },
+    {
+      name: "authenticated",
+      testMatch: /\.spec\.ts$/,
+      testIgnore: /public\.spec\.ts$/,
+      dependencies: ["setup"],
+      use: {
+        ...devices["Desktop Chrome"],
+        storageState: "e2e/.auth/user.json",
+      },
+    },
+  ],
+});