fix(ci): e2e — let Playwright manage both servers (fixes the 2-hour hang)

The e2e job backgrounded `dotnet run &` and `ng serve &` in separate Actions
steps, then `npx wait-on` (no timeout) in a later step. A process started with
`&` in one step is killed when that step's shell exits, so wait-on waited forever
on servers that were already gone — the job hung until the runner's hard limit
(~2h; Gitea's act_runner doesn't reliably enforce timeout-minutes).

Move both servers into Playwright's `webServer` (an array: backend + `npm start`),
so Playwright starts them, waits for readiness, runs the suite, and tears them
down in the one `npm run e2e` process — CI and local alike. The CI e2e job is now
just npm ci / playwright install / npm run e2e. `reuseExistingServer` is on locally
(reuses a running app, incl. the docker stack) and off in CI (fresh start).

Verified locally via `CI=1 npm run e2e` against free ports + a clean db: both
smoke tests pass in ~15s (no hang). The earlier local failure was leftover SQLite
state (WP-22) from a dirty run resuming a Concept — CI checks out fresh, so its db
is always empty.

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

playwright.config.ts

@@ -15,15 +15,26 @@ export default defineConfig({
     trace: 'on-first-retry',
   },
   projects: [{ name: 'chromium', use: { browserName: 'chromium' } }],
-  // CI starts `ng serve` + the backend as separate job steps (both need to be up
-  // before the suite runs); locally, boot `npm start` automatically so `npm run e2e`
-  // works standalone — the backend still needs `dotnet run` running separately.
-  webServer: process.env['CI']
-    ? undefined
-    : {
-        command: 'npm start',
-        url: baseURL,
-        reuseExistingServer: true,
-        timeout: 120_000,
-      },
+  // Playwright owns both servers' lifecycle — start, wait-for-ready, tear down — in the
+  // one `npm run e2e` process, so `npm run e2e` is self-contained locally AND in CI.
+  // Do NOT background them as separate CI steps: a process started with `&` in one
+  // Actions `run:` step is killed when that step's shell exits, so a later `wait-on`
+  // step hangs forever on servers that are already gone (the 2-hour e2e hang).
+  // `reuseExistingServer` locally lets you run against an already-running app (incl. the
+  // docker stack on 4200/5000); CI always starts fresh. Backend gets a longer timeout —
+  // `dotnet run` cold-restores+builds before it listens.
+  webServer: [
+    {
+      command: 'dotnet run --project backend/src/BigRegister.Api --urls http://localhost:5000',
+      url: 'http://localhost:5000/swagger',
+      reuseExistingServer: !process.env['CI'],
+      timeout: 180_000,
+    },
+    {
+      command: 'npm start',
+      url: baseURL,
+      reuseExistingServer: !process.env['CI'],
+      timeout: 120_000,
+    },
+  ],
 });