test(app): more e2e tests

packages/app/e2e/home.spec.ts

@@ -1,6 +1,24 @@
 import { test, expect } from "@playwright/test"
 
-test("home shows recent projects header", async ({ page }) => {
+test("home renders and shows an open project entrypoint", async ({ page }) => {
   await page.goto("/")
-  await expect(page.getByText("Recent projects")).toBeVisible()
+
+  await expect(page.getByText("Recent projects").or(page.getByText("No recent projects"))).toBeVisible()
+  await expect(page.getByRole("button", { name: "Open project" }).first()).toBeVisible()
+})
+
+test("server picker dialog opens from home", async ({ page }) => {
+  const host = process.env.PLAYWRIGHT_SERVER_HOST ?? "localhost"
+  const port = process.env.PLAYWRIGHT_SERVER_PORT ?? "4096"
+  const name = `${host}:${port}`
+
+  await page.goto("/")
+
+  const trigger = page.getByRole("button", { name })
+  await expect(trigger).toBeVisible()
+  await trigger.click()
+
+  const dialog = page.getByRole("dialog", { name: "Servers" })
+  await expect(dialog).toBeVisible()
+  await expect(dialog.getByPlaceholder("Search servers")).toBeVisible()
 })